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P3-Factorization of complete bipartite graphs
1988
Discrete Mathematics
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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
1998
Discrete Mathematics
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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]
2018
arXiv
pre-print
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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
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. 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
2004
Discrete Mathematics
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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
2004
Discrete Mathematics
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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
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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
2015
International Journal of Soft Computing, Mathematics and Control
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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
1980
Theoretical Computer Science
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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
2014
Proceedings of the 8th ACM Conference on Recommender systems - RecSys '14
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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
2012
Mapana Journal of Sciences
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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
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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
1994
Discrete Mathematics
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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]
2021
arXiv
pre-print
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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
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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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