Results 31 to 40 of about 11,475 (265)
Two extensions of Ramsey's theorem [PDF]
, 2012 Ramsey's theorem, in the version of Erd\H{o}s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2,...,n} contains a monochromatic clique of order 1/2\log n.
Conlon, David +2 more
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Lower Estimate of Clique Size via Edge Coloring [PDF]
Mathematica Pannonica, 2021 In many clique search algorithms well coloring of the nodes is employed to find an upper bound of the clique number of the given graph. In an earlier work a non-traditional edge coloring scheme was proposed to get upper bounds that are typically better than the one provided by the well coloring of the nodes.
Király, Balázs, Szabó, Sándor
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Graphs with Strong Proper Connection Numbers and Large Cliques
Axioms, 2023 In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=n−i for 1⩽i⩽3. Next, we investigate the rainbow
Yingbin Ma, Xiaoxue Zhang, Yanfeng Xue
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Lessons from the Congested Clique Applied to MapReduce [PDF]
, 2014 The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed $O(\Delta)$-coloring ...
A. Berns +10 more
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Applying Graph Neural Networks to the Decision Version of Graph Combinatorial Optimization Problems
IEEE Access, 2023 In recent years, there has been a significant increase in the application of graph neural networks on a wide range of different problems. A specially promising direction of research is on graph convolutional neural networks (GCN).
Raka Jovanovic +3 more
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Unique Colorability and Clique Minors [PDF]
Journal of Graph Theory, 2016 AbstractFor a graph G, let denote the largest k such that G has k pairwise disjoint pairwise adjacent connected nonempty subgraphs, and let denote the largest k such that G has k pairwise disjoint pairwise adjacent connected subgraphs of size 1 or 2. Hadwiger's conjecture states that , where is the chromatic number of G. Seymour conjectured for all
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Cliques with many colors in triple systems [PDF]
Journal of Combinatorics, 2021 Erd s and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and R dl asked whether there is some integer $q\ge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset ...
Mubayi, Dhruv, Suk, Andrew
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On a k-clique-join of a class of partitionable graphs [PDF]
Computer Science Journal of Moldova, 2005 We call a graph G O-graph if there is an optimal coloring of the set of vertices and an optimal (disjoint) covering with cliques such that any class of colors intersects any clique.
Mihai Talmaciu
doaj
Some results on the total proper k-connection number
Open Mathematics, 2022 In this paper, we first investigate the total proper connection number of a graph GG according to some constraints of G¯\overline{G}. Next, we investigate the total proper connection numbers of graph GG with large clique number ω(G)=n−s\omega \left(G)=n ...
Ma Yingbin, Zhang Hui
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A Different Short Proof of Brooks’ Theorem
Discussiones Mathematicae Graph Theory, 2014 Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.
Rabern Landon
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