Results 11 to 20 of about 11,451 (248)
On equitable near-proper coloring of some derived graph classes
Karpatsʹkì Matematičnì Publìkacìï, 2022 An equitable near-proper coloring of a graph $G$ is a defective coloring in which the number of vertices in any two color classes differ by at most one and the bad edges obtained is minimized by restricting the number of color classes that can have ...
S. Jose, S. Naduvath
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A note on r-equitable k-colorings of trees [PDF]
Yugoslav Journal of Operations Research, 2014 A graph G = (V;E) is r-equitably k-colorable if there exists a partition of V into k independent sets V1, V2,... Vk such that ||Vi|- |Vj|| ≤ r for all i,j {1,2... k}.
Hertz Alain, Ries Bernard
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Equitable Coloring of IC-Planar Graphs with Girth g ≥ 7
Axioms, 2023 An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most 1. If there is an equitable k-coloring of G, then the graph G is said to be equitably k-colorable.
Danjun Huang, Xianxi Wu
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Perfect 2-colorings of the generalized Petersen graph GP(n,3)
Electronic Journal of Graph Theory and Applications, 2022 In this paper we enumerate the parameter matrices of all perfect 2-colorings of the generalized Petersen graphs GP(n, 3), where n ≥ 7. We also give some basic results for GP(n, k).
Hamed Karami
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A tabu search heuristic for the Equitable Coloring Problem [PDF]
, 2014 The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several applications.
A Hajnal +16 more
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Equitable Coloring of Sparse Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2010 In the journal version, Lemma 3.1 is incorrect as stated, so in the current version we replaced its unique use (in the proof of Lemma 3.2) by a direct argument and removed Lemma 3.1.
Luo, Rong +3 more
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Journal of Combinatorial Theory, Series B, 1994 A graph \(G\) is said to be equitably \(k\)-colourable if the vertices of \(G\) can be partitioned into \(k\) independent sets \(V_ i\) such that \(\| V_ i | - | V_ j \| \leq 1\) for all \(i\) and \(j\). We regard a non-null tree \(T\) as a bipartite graph \(T(X,Y)\). The authors show that \(T\) is equitably \(k\)-colourable if and only if \[ k \geq 2 \
Chen, B.L., Lih, K.W.
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Equitable and semi-equitable coloring of cubic graphs and its application in batch scheduling
Archives of Control Sciences, 2015 In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NP-complete within a broad spectrum ...
Furmańczyk Hanna, Kubale Marek
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On the Strong Equitable Vertex 2-Arboricity of Complete Bipartite Graphs
Mathematics, 2020 An equitable partition of a graph G is a partition of the vertex set of G such that the sizes of any two parts differ by at most one. The strong equitable vertexk-arboricity of G, denoted by vak≡(G), is the smallest integer t such that G can be equitably
Fangyun Tao, Ting Jin, Yiyou Tu
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Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A graph $G$ is equitably $k$-choosable if, for any given $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $\lceil\frac{|V(G)|}{k}\rceil$ vertices.
Aijun Dong, Jianliang Wu
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