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The number of matchings in random regular graphs and bipartite graphs

B Bollobás, B.D McKay
<span title="">1986</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
Then the average number of l-factors in a random regular bipartite graph of degree n  ...  Our main aim in this paper is to determine the asymptotic values of the first two moments of the number of l-factors in random regular graphs and bipartite graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(86)90029-8">doi:10.1016/0095-8956(86)90029-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zxztigkyjzcwzjqvvkknueabpu">fatcat:zxztigkyjzcwzjqvvkknueabpu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928194942/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/6c3/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDk1ODk1Njg2OTAwMjk4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ac/c4/acc45fcb0ab0474c27de95e39095ddd175d64215.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(86)90029-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Packing tree factors in random and pseudo-random graphs [article]

Deepak Bal, Alan Frieze, Michael Krivelevich, Po-Shen Loh
<span title="2014-04-01">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that for a fixed tree T on t vertices and ϵ > 0, the random graph G_n,p, with n a multiple of t, with high probability contains a family of edge-disjoint T-factors covering all but an ϵ-fraction  ...  For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of  ...  Note that the vertex disjointness implies that the vertex set of the H-factor, H 1 ∪ • • • ∪ H n/t , is equal to V . H-factors have been an important object in the study of random graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1304.2429v2">arXiv:1304.2429v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7ldnzudfxbhcjkwunmdao5i5ji">fatcat:7ldnzudfxbhcjkwunmdao5i5ji</a> </span>
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Packing Tree Factors in Random and Pseudo-Random Graphs

Deepak Bal, Alan Frieze, Michael Krivelevich, Po-Shen Loh
<span title="2014-04-16">2014</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
We prove that for a fixed tree $T$ on $t$ vertices and $\epsilon>0$, the random graph $G_{n,p}$, with $n$ a multiple of $t$, with high probability contains a family of edge-disjoint $T$-factors covering  ...  For a fixed graph $H$ with $t$ vertices, an $H$-factor of a graph $G$ with $n$ vertices, where $t$ divides $n$, is a collection of vertex disjoint (not necessarily induced) copies of $H$ in $G$ covering  ...  of Theorem 1 for pseudo-random graphs gives a packing result for random graphs with p n −1/4 log 3/4 n.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/3285">doi:10.37236/3285</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wuu3slpbuzaujhjws67uka7nym">fatcat:wuu3slpbuzaujhjws67uka7nym</a> </span>
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On large-girth regular graphs and random processes on trees

Ágnes Backhausz, Balázs Szegedy
<span title="2018-02-27">2018</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wtbq2zeu3fctdhu67pe2vn6hti" style="color: black;">Random structures &amp; algorithms (Print)</a> </i> &nbsp;
We study various classes of random processes defined on the regular tree T d that are invariant under the automorphism group of T d .  ...  Using this correspondence principle together with entropy inequalities for typical processes, we prove that there are no approximative covering maps from random d-regular graphs to d-regular weighted graphs  ...  The research was supported by the MTA Rényi Institute Lendület Limits of Structures Research Group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/rsa.20769">doi:10.1002/rsa.20769</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/itvf3ioa6fdtjo4jqmgt5eian4">fatcat:itvf3ioa6fdtjo4jqmgt5eian4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427182535/http://real.mtak.hu/89854/1/1406.4420v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/37/78/3778df69c0acc75f2663db1f0a31629b22540624.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/rsa.20769"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

On large girth regular graphs and random processes on trees [article]

Ágnes Backhausz, Balázs Szegedy
<span title="2015-07-27">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Using this correspondence principle together with entropy inequalities for typical processes we prove a family of combinatorial statements about random d-regular graphs.  ...  We study various classes of random processes defined on the regular tree T_d that are invariant under the automorphism group of T_d.  ...  The research was supported by the MTA Rényi Institute Lendület Limits of Structures Research Group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.4420v2">arXiv:1406.4420v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7oeriybmjfd55ei36imiiqebiy">fatcat:7oeriybmjfd55ei36imiiqebiy</a> </span>
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1-factorizations of pseudorandom graphs [article]

Asaf Ferber, Vishesh Jain
<span title="2018-03-28">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we consider the problem of finding 1-factorizations of regular, pseudorandom graphs.  ...  In particular, since (as is well known) a typical random d-regular graph G_n,d is such a graph, we obtain the existence of a 1-factorization in a typical G_n,d for all C_0≤ d≤ n-1, thereby extending to  ...  H ′ t are regular balanced bipartite graphs, and F is a 1-factorization of the regular graph G\ t i=1 H ′ i , we would be done.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.10361v1">arXiv:1803.10361v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/src4qm5kazd6pixztnwh2bzczm">fatcat:src4qm5kazd6pixztnwh2bzczm</a> </span>
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Cover Time and Broadcast Time [article]

Robert Elsässer, Thomas Sauerwald
<span title="2009-02-10">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For any δ-regular (or almost δ-regular) graph G it holds that R(G) = Ω(δ^2/n·1/ n).  ...  CRRST97 that "the cover time of the graph is an appropriate metric for the performance of certain kinds of randomized broadcast algorithms".  ...  For any regular graph G = (V, E), COV(G) = O( 1 1−λ 2 · n log n). Randomized Broadcast.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.1735v1">arXiv:0902.1735v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/imiv5mbpinacdc2me6v5igzike">fatcat:imiv5mbpinacdc2me6v5igzike</a> </span>
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Page 5943 of Mathematical Reviews Vol. , Issue 89K [page]

<span title="">1989</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this note the author proposes the concept of L-transformation on directed 1-factors of a digraph D, introduces the definition of the directed 1-factor graph M(D) of D, and proves that M(D) is isomorphic  ...  A 4-regular graph of diameter 2 is called strongly regular. Such a graph with v vertices and with regularity degree k is said to have the parameters (v,k,A, 1).  ... 
<span class="external-identifiers"> </span>
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Local law for eigenvalues of random regular bipartite graphs [article]

Linh V. Tran
<span title="2013-10-17">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we study the local law for eigenvalues of large random regular bipartite graphs with degree growing arbitrarily fast.  ...  We prove that the empirical spectral distribution of the adjacency matrix converges to a scaled down copy of the Marchenko - Pastur distribution on intervals of short length.  ...  This is a bipartite analogue of the popular random regular graph model, which is a random graph sampled uniformly from the set of all regular graphs on the same set of vertices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.4606v1">arXiv:1310.4606v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lnvfcabzhvafxcukqj2ytvrevi">fatcat:lnvfcabzhvafxcukqj2ytvrevi</a> </span>
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On one-factorizations of replacement products

Alireza Abdollahi, Amir Loghman
<span title="">2013</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
If the set of edges of a graph can be partitioned to a set of complete matchings, then the graph is called 1-factorizable and any such partition is called a 1-factorization.  ...  Let G be an (n, m)-graph (n vertices and m-regular) and H be an (m, d)-graph. Randomly number the edges around each vertex of G by {1, . . . , m} and fix it.  ...  The authors are grateful to the referee for his/her invaluable comments improving the original version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1301057a">doi:10.2298/fil1301057a</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q7gcinnugbgzzpfhayryy6woli">fatcat:q7gcinnugbgzzpfhayryy6woli</a> </span>
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Satisfiability Thresholds for Regular Occupation Problems

Konstantinos Panagiotou, Matija Pasch, Michael Wagner
<span title="2019-07-08">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
The two most popular types of such CSPs are the Erdős-Rényi and the random regular CSPs.  ...  The regular r-in-k occupation problems resemble a basis of this class.  ...  Further, randomized polynomial time algorithms for the generation and approximate counting of 2-factors in random regular simple graphs have been introduced in [25] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.90">doi:10.4230/lipics.icalp.2019.90</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/PanagiotouP19.html">dblp:conf/icalp/PanagiotouP19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tvqr6ugbhveqdpkemm5ybrsiiy">fatcat:tvqr6ugbhveqdpkemm5ybrsiiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220307212224/https://drops.dagstuhl.de/opus/volltexte/2019/10666/pdf/LIPIcs-ICALP-2019-90.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/30/7c/307c5af44e57cfa075e89ba4dbee38849fd3eea0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.90"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

MODELING THE PERFORMANCE OF COMMUNICATION SCHEMES ON NETWORK TOPOLOGIES

JAN LEMEIRE, ERIK DIRKX, WALTER COLITTI
<span title="">2008</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x6p3xmf7graczk5begbrisonce" style="color: black;">Parallel Processing Letters</a> </i> &nbsp;
The property allows the accurate quantitative prediction of the runtime of random communication on random topologies.  ...  Each NT i is characterized by a Performance Factor, called  ...  Most graphs have a factor that is more than 1, which indicates that the communication time is higher than that of random graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s012962640800334x">doi:10.1142/s012962640800334x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cn2gwemqe5covfsc7jk6escg3i">fatcat:cn2gwemqe5covfsc7jk6escg3i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809103021/http://parallel.vub.ac.be/~jan/papers/JanLemeire_ModelingPerformanceCommunicationOnTopologies_PPL_june2008.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/df/8b/df8b734568d1635fcac5d81bf1366bdb6a1310a1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s012962640800334x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

3-star factors in random d-regular graphs

Hilda Assiyatun, Nicholas Wormald
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
In this paper, we use the method to prove the almost sure existence of 3-star factors in random d-regular graphs.  ...  Since then it has been used to study the almost sure existence of, and the asymptotic distribution of, regular spanning subgraphs of various types in random d-regular graphs and hypergraphs.  ...  Acknowledgements The authors are thankful to the referees for a number of comments that helped to improve the presentation of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2006.05.003">doi:10.1016/j.ejc.2006.05.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/masqptwjr5e3nli2nfbovzh3ai">fatcat:masqptwjr5e3nli2nfbovzh3ai</a> </span>
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Tight products and graph expansion

Amit Daniely, Nathan Linial
<span title="2011-02-18">2011</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ukzsjb6a6zhyxnjl6nb2mmjc6m" style="color: black;">Journal of Graph Theory</a> </i> &nbsp;
This perspective yields a new characterization of class-1 (2k +1)-regular graphs. We also obtain a new model of random d-regular graphs whose second eigenvalue is almost surely at most O(d 3/4 ).  ...  A graph H is said to be a tight product of two (undirected multi) graphs G 1 and G 2 , if V (H) = V (G 1 )×V (G 2 ) and both projection maps V (H) → V (G 1 ) and V (H) → V (G 2 ) are covering maps.  ...  Class-1 graphs (The (G)-edge-coloring will do). 2. 2k-regular graphs (Find a 2-factorization and color the ith factor half i half k +i). 3. (2k +1)-regular graphs containing a perfect matching (Use one  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921211626/http://www.cs.huji.ac.il/%7Enati/PAPERS/tight_products.pdf?origin%3Dpublication_detail" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/de/77de616968dcabd0721da8e1cfe0933cf4ef866c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jgt.20593"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

On the Quality of Sampling from Geographic Networks

Gunes Ercal, John Matta, William Stimson, Dominic Eccher
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cx3f4s3qmfe6bg4qvuy2cxezyu" style="color: black;">Procedia Computer Science</a> </i> &nbsp;
We ask in particular what factor most affects the sampling quality: The distribution of the nodes in the space or the connectivity structure of the links?  ...  We consider the problem of randomly sampling information from a network embedded in two-dimensional space, as characteristic of a physical network.  ...  For d-regular graphs, the random walk process is defined by a Markov chain that is identical to the normalized adjacency matrix, namely A multiplied by 1/d.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procs.2013.09.313">doi:10.1016/j.procs.2013.09.313</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d6t2uqgnlnf3ndhv4km2i2ufs4">fatcat:d6t2uqgnlnf3ndhv4km2i2ufs4</a> </span>
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