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P3-Factorization of complete bipartite graphs

Kazuhiko Ushio
1988 Discrete Mathematics  
In this paper, it is shown that a necessary and sufficient condition for the existence of a P,-factorization of K"" is (i) m + n -0 (mod 3), (ii) m < 2n, (iii) n s 2m and (iv) 3mn/2(m + n) is an integer  ...  Introduction Let P3 be a path on 3 points and K,,,, be a complete bipartite graph with partite sets VI and V,, where IV,1 = m and IV,/ = n.  ...  In this graph, two points are adjacent if and only if the subsets come from disjoint independent sets of K,,,,,. G is a complete bipartite graph KS,,.  ... 
doi:10.1016/0012-365x(88)90227-0 fatcat:gzzklvbl45ejrnt2fe72v4rdfi

Imbeddings of the tensor product of graphs where the second factor is a complete graph

Ghidewon Abay Asmerom
1998 Discrete Mathematics  
In this paper we present genus result for the tensor product of graphs where the second factor is the complete graph Km and m is a power of 2.  ...  The genus of H ® K." where H is a graph with a quadrilateral imbedding and also H is either, bipartite, with bichromatic dual, or with straight-ahead imbedding is given *  ...  In this paper we will use the surgical-voltage method to find the genus parameter for the tensor product of graphs when one of the factors is Kin, the complete graph on m vertices where m is a power of  ... 
doi:10.1016/s0012-365x(97)00130-1 fatcat:qqjsgziwo5eyblhlwtkhpoxvza

Perfect weak modular product graphs [article]

Danial Dervovic
2018 arXiv   pre-print
Interesting cases include complete multipartite graphs and disjoint unions of cliques.  ...  The weak modular product differs from the direct product by also encoding non-adjacencies of the factor graphs in its edges.  ...  The software SageMath [Sage] has been invaluable to this work, alongside the ISGCI graph database [ISGCI].  ... 
arXiv:1809.09939v1 fatcat:25tp4y5xlveerdsowfhp7geu4u

Page 1724 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
. the existence of a P3-factorization of the symmetric complete * myn?  ...  Summary: “In this paper, a necessary and sufficient condition for the existence of a P3-factorization of the complete bipartite multigraph AK,,,, and a necessary and sufficient condition for . ——- . .  ... 

Packing paths of length at least two

M. Kano, G.Y. Katona, Z. Király
2004 Discrete Mathematics  
vertices of the original graph.  ...  We give a simple proof for Kaneko's theorem which gives a su cient and necessary condition for the existence of vertex disjoint paths in a graph, each of length at least two, that altogether cover all  ...  result of Kaneko and started to work on this paper.  ... 
doi:10.1016/j.disc.2004.01.016 fatcat:gena2ana7zhzbhrijfbj34hkhe

Packing paths of length at least two

M KANO
2004 Discrete Mathematics  
vertices of the original graph.  ...  We give a simple proof for Kaneko's theorem which gives a su cient and necessary condition for the existence of vertex disjoint paths in a graph, each of length at least two, that altogether cover all  ...  result of Kaneko and started to work on this paper.  ... 
doi:10.1016/s0012-365x(04)00152-9 fatcat:sdx5yermf5gutcp5ljibjsnofm

Page 8208 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Gary MacGillivray (3-VCTR; Victoria, BC) 99m:05119 05C70 Du, Beiliang (PRC-SOO; Suzhou) P3-factorization of complete multipartite graphs.  ...  Summary: “In this note it is shown that a necessary and sufficient condition for the existence of a P3-factorization of the complete multipartite graph AK” is (1) m > 3, (2) mn =0 (mod 3) and (3) m A(m  ... 

Expression of Composite Number as Primes Using Hyper Graphs

Meenakshi K, Harisha CS
2015 International Journal of Soft Computing, Mathematics and Control  
KEY WORDS prime factorization theorem, complete prime vertex composite edge weighted hypergraph  ...  The prime factorization theorem states that every integer greater than 1 can be expressed as a product of primes.  ...  The prime factorization is not unique in case of connected bipartite graphs. They have proved that prime factorization of a connected bipartite graph has exactly one bipartite factor.  ... 
doi:10.14810/ijscmc.2015.4101 fatcat:bqdgxooeozhcnlwiuul2bwqf3q

On another Boolean matrix

Nicholas Pippenger
1980 Theoretical Computer Science  
In his paper "On a Boolean matrix", Nechiporuk gave an explicit example of a set of n homogeneous monotone Boolean functions of the first degree in n variables that require f2(n3'*) two-input gates in  ...  The conditions we desire for Boolean matrices can then be translated into conditions on bipartite graphs; specifically, we seek bipartite graphs that have many edges but no large complete bipartite subgraphs  ...  Nechiporuk's results then follow from a construction (due to Sos and Turin [3] ) of a bipartite graph with n(n"') edges but no copy of K2,* (that is, no complete bipartite subgraph with 2 inputs and 2  ... 
doi:10.1016/0304-3975(80)90034-1 fatcat:tuynnafxdbfovdhnrjuyg6sr7u

GASGD

Fabio Petroni, Leonardo Querzoni
2014 Proceedings of the 8th ACM Conference on Recommender systems - RecSys '14  
of 18 Graph representation I The rating matrix describes a bipartite graph.  ...  Bipartite Aware Greedy Algorithm I Real word bipartite graphs are often significantly skewed: one of the two sets is much bigger than the other.  ...  Communication cost I T = the training set I U = users set I I = items set I V = U [ I I C = processing nodes I RF = replication factor I RF U = users' RF of 18 Conclusions I three distinct contributions  ... 
doi:10.1145/2645710.2645725 dblp:conf/recsys/PetroniQ14 fatcat:45lahsgcznhylbedntd4aqvgey

A Comparison on the Bounds of Chromatic Preserving Number and Dom-Chromatic Number of Cartesian Product and Kronecker Product of Paths

T N Janakiraman, M Poobalaranjani
2012 Mapana Journal of Sciences  
The Kronecker product G1 Ù G2 of two graphs G1 = (V1, E1) and G2 = (V2, E2) is the graph G with vertex set V1 x V2 and any two distinct vertices (u1, v1) and (u2, v2) of G are adjacent if u1u2 Î E1 and  ...  The minimum cardinality of a dom-chromatic set in a graph G is called the dom-chromatic number (or dc- number) of G and is denoted by γch(G).  ...  The complete graph K2 is an example of a 2-critical graph and odd cycles are 3-critical graphs.  ... 
doi:10.12723/mjs.23.3 fatcat:2qxstasa45fhzdggrvuu3jabwu

Page 7839 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Kaneko gave a necessary and sufficient condition for a graph to have a {P3, Ps, Ps}-factor. As a corollary, he proved that every cubic graph has a { P3, Py, Ps}-factor.  ...  (I-BASI; Potenza) On determinants and permanents of minimally 1-factorable cubic bipartite graphs. (English summary) Note Mat. 20 (2000/01), no. 1, 37—42.  ... 

On the genus of the tensor product of graphs where one factor is a regular graph

Tamara Dakić, Tomaž Pisanski
1994 Discrete Mathematics  
This construction can also be extended to the tensor product HOG where G is a (2k+ 1)-regular graph with l-factor.  ...  Assuming that H is suitably imbedded in some orientable surface by modifying the edges of H according to the configuration of G we get the permutation voltage graph H c2') whose permutation derived graph  ...  Here we try to extend this construction to the tensor product of graphs where one of the factors is either 2k-regular or (2k+ 1)-regular graph with a l-factor.  ... 
doi:10.1016/0012-365x(93)e0057-b fatcat:7ehxteqeanayxex6q5jinfa3am

Quasirandom Graphs and the Pantograph Equation [article]

Asaf Shapira, Mykhaylo Tyomkyn
2021 arXiv   pre-print
This provides a natural example of an infinite family of graphs, which is not forcing, and answers a natural question posed by P. Horn.  ...  In this article we describe a new surprising application of these objects in graph theory, by showing that the set of all cliques is not forcing for quasirandomness.  ...  If G is a complete bipartite graph 1 with both parts of size n/2, where n is a large even number, and H is a star with k edges, i.e., a complete bipartite graph with part sizes 1 and k, then G contains  ... 
arXiv:2101.08173v2 fatcat:7zbcytkbnvc3td7rk2wrd4o56y

Page 623 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
A bipartite directed graph D is said to be complete bipartite if each pair of vertices from different bipartition classes of D is joined by at least one edge.  ...  A directed graph is said to be traceable if it has a directed Hamiltonian path. The main theorem states that a complete bipartite directed graph D is traceable if and only if it has an almost-factor.  ... 
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