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An improvement on Łuczak's connected matchings method [article]

Shoham Letzter
2022 arXiv   pre-print
A connected matching in a graph G is a matching contained in a connected component of G.  ...  We show that these can be further reduced to problems about monochromatic connected matchings in complete graphs.  ...  A connected matching is a matching contained in a connected component.  ... 
arXiv:2009.03119v4 fatcat:iesjvearevcapn6hg7ohkdiy5m

Matching integral 2-connected graphs [article]

Ebrahim Ghorbani
2021 arXiv   pre-print
In this note we present an infinite family of 2-connected graphs such that their matching polynomials have only integer zeros. This answers in negative a question of Akbari et al.  ...  [Graphs with integer matching polynomial zeros, Discrete Appl. Math. 224 (2017), 1-8].  ...  This shows that H k is a matching integral graph. Figure 2: A 3-connected matching integral graph A natural generalization would be looking for matching integral graphs with higher connectivity.  ... 
arXiv:2109.04118v2 fatcat:lpivsvgu7bcjpeg2wv2jud24mq

Matching Humans with Different Connectivity

S. Melzi, R. Marin, E. Rodolà, U. Castellani, J. Ren, A. Poulenard, P. Wonka, M. Ovsjanikov
2019 Eurographics Workshop on 3D Object Retrieval, EG 3DOR  
Our evaluation proves that connectivity changes lead to Objects Matching difficulties and we hope this will promote further research in matching shapes with wildly different connectivity.  ...  This track provides the first matching evaluation in terms of large connectivity changes between models that come from totally different modeling methods.  ...  Methods Point-to-point matching is performed i) by computing point descriptors and matching those in descriptor space, or ii) by designing a matching pipeline.  ... 
doi:10.2312/3dor.20191070 fatcat:hr2taefhq5hjhor5qldf63qp44

Videoamplifier with matched connecting impedances

I. Yu. Malevich, D. A. Solonovich
2019 Doklady BGUIR  
The results of the logical-heuristic synthesis, development and laboratory tests of a video amplifier with a large dynamic range for the matched receiving paths of radio systems are presented.  ... 
doaj:a7fdb493717d4c2c8e100823a9c56490 fatcat:gvikgxrix5e7xho5ebusfqnana

Connected matchings and Hadwiger's conjecture

2005 Combinatorics, probability & computing  
a connected matching of size t.  ...  . , e t of G is called a connected matching of size t ( [8] ) if for every 1 ≤ i < j ≤ t there exists at least one edge of G connecting an endpoint of e i to an endpoint of e j .  ... 
doi:10.1017/s0963548305006759 fatcat:rswsy5fk6nbzzk7bf6nvidwhgy

Matching Connectivity: On the Structure of Graphs with Perfect Matchings [article]

Archontia C. Giannopoulou, Stephan Kreutzer, Sebastian Wiederrecht
2019 arXiv   pre-print
We introduce some basic properties of matching connectivity and prove a Menger-type result for matching n-connected graphs.  ...  We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings.  ...  Notice that since G is matching n-connected then cov(G) is matching n-connected and thus cov(G) is matching n-connected.  ... 
arXiv:1704.00493v2 fatcat:w3s6c42sy5dknfegpesyxmdwfq

Cuts in matchings of 3-connected cubic graphs [article]

Kolja Knauer, Petru Valicov
2018 arXiv   pre-print
We show that all of them fit into the same framework related to cuts in matchings.  ...  conjectures on Hamiltonicity in cubic graphs (Tait, Barnette, Tutte), on the dichromatic number of planar oriented graphs (Neumann-Lara), and on even graphs in digraphs whose contraction is strongly connected  ...  Every 3-connected, cubic, planar digraph contains a perfect matching without a directed cut. Conjecture V (Hochstättler).  ... 
arXiv:1712.06143v3 fatcat:bwxfo2mwkfc6xm64eyzw6owfr4

Super edge-connectivity and matching preclusion of data center networks [article]

Huazhong Lü, Tingzeng Wu
2019 arXiv   pre-print
Moreover, as an application of k-restricted edge-connectivity, we study the matching preclusion number and conditional matching preclusion number, and characterize the corresponding optimal solutions of  ...  Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. k-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks  ...  Particularly, has proved recently that it is NP-complete to determine the matching preclusion number and conditional matching preclusion number of a connected bipartite graph.  ... 
arXiv:1807.05224v5 fatcat:zi6ruhhu7jea5kuqslhp32v5pq

Ramsey Numbers of Connected Clique Matchings [article]

Barnaby Roberts
2016 arXiv   pre-print
We determine the Ramsey number of a connected clique matching.  ...  That is, we show that if G is a 2-edge-coloured complete graph on (r^2 - r - 1)n - r + 1 vertices, then there is a monochromatic connected subgraph containing n disjoint copies of K_r, and that this number  ...  The connectivity requirement here proves to be very significant as for large values of r the Ramsey number of a connected K r -matching is approximately r/2 times larger than that of a standard K r -matching  ... 
arXiv:1605.07492v1 fatcat:iqpccigpi5fhnfnn7fb6ybz5qa

Perfect matchings in highly cyclically connected regular graphs [article]

Robert Lukoťka, Edita Rollová
2021 arXiv   pre-print
A leaf matching operation on a graph consists of removing a vertex of degree 1 together with its neighbour from the graph.  ...  For k≥ 0, let G be a d-regular cyclically (d-1+2k)-edge-connected graph of even order.  ...  In this paper, we study perfect matchings of highly connected regular graphs.  ... 
arXiv:1709.08891v2 fatcat:fm2v5f4375hjzdoy5bccpxdmc4

Connectivity measures in matched sum graphs

C. Balbuena, P. García-Vázquez, X. Marcote
2008 Discrete Mathematics  
In this paper, we derive lower bounds for the connectivity, edge-connectivity, and different conditional connectivities in matched sum graphs, and present sufficient conditions which guarantee maximum  ...  values for these conditional connectivities.  ...  Clearly, G 1 and G 2 connected yield a connected matched sum graph G = G 1 ∪ f G 2 . Theorem 2.1.  ... 
doi:10.1016/j.disc.2007.04.051 fatcat:lgzanfehabawhizmtjdwxw3zcy

Matching preclusion for cube-connected cycles

Qiuli Li, Wai Chee Shiu, Haiyuan Yao
2015 Discrete Applied Mathematics  
We consider matching preclusion of cube-connected cycles network CCC n .  ...  By using the super-edge-connectivity of vertex-transitive graphs, the super cyclically edge-connectivity of $CCC_{n}$ for $n=3,4$ and 5, Hall's Theorem and the strengthened Tutte's Theorem, we obtain the  ...  Meanwhile, matching preclusion number has a theoretical connection with conditional connectivity and "changing and unchanging of invariants".  ... 
doi:10.1016/j.dam.2015.04.001 fatcat:7qcau2l4xjej7dh2c4nudqinuq

Comparing brains by matching connectivity profiles

Rogier B. Mars, Lennart Verhagen, Thomas E. Gladwin, Franz-Xaver Neubert, Jerome Sallet, Matthew F.S. Rushworth
2016 Neuroscience and Biobehavioral Reviews  
We exploit the fact that cortical regions can be characterized by the unique pattern of connectivity, the so-called connectivity fingerprint.  ...  Here, we present an approach to formally comparing the connectivity of different cortical areas across different brains.  ...  Matching macaque F6 connectivity fingerprint to voxels across a cortical territory.  ... 
doi:10.1016/j.neubiorev.2015.10.008 pmid:26627865 pmcid:PMC6485474 fatcat:z3c5vaiz5va4tp2cwyezmp4454

Connections between Wiener index and matchings

Weigen Yan, Yeong-Nan Yeh
2005 Journal of Mathematical Chemistry  
In this work, we show that the Wiener index of T can be explained as the number of matchings with n − 2 edges in S(T ). Furthermore, some related results are also obtained.  ...  The above result connects the Wiener index (a quantity defined on the basis of graph distances) and matrix eigenvalues. The possible chemical implications of (6) were discussed in [19, 20] .  ...  Hence, by induction, S(T − u) − v contains a perfect matching, denoted by M 1 . It is obvious that S(T )−v contains a perfect matching M 1 ∪ {(u, e 1 )}.  ... 
doi:10.1007/s10910-005-9026-0 fatcat:dikqseo52jdt3c6763l4dgted4

Signal classification by matching node connectivities

Linh Lieu, Naoki Saito
2009 2009 IEEE/SP 15th Workshop on Statistical Signal Processing  
Our proposed Node Connectivity Matching (NCM) method is derived from the diffusion distance.  ...  To classify an unlabeled data point, we compare its node connectivities to the training histograms using the L 2 norm as a bin-by-bin histogram discriminant measure.  ...  Finally we illustrate an application of our proposed Node Connectivity Matching (NCM) method in Sec. 5.  ... 
doi:10.1109/ssp.2009.5278633 fatcat:nkphvaepi5b4jgtb3dsuhesokq
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