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New Results on the Robust Coloring Problem
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and...
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Equitable Colorings of Hypergraphs with r Colors
The paper deals with a problem concerning equitable vertex colorings of uniform hypergraphs, i.e., colorings under which there are no monochromatic...
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Equitable Clique-Coloring in Claw-Free Graphs with Maximum Degree at Most 4
A clique of a graph G is a set of pairwise adjacent vertices of G . A clique-coloring of G is an assignment of colors to the vertices of G in such a...
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Equitable Vertex Arboricity Conjecture Holds for Graphs with Low Degeneracy
The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely,...
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On the Equitable Choosability of the Disjoint Union of Stars
Equitable k -choosability is a list analogue of equitable k -coloring that was introduced by Kostochka et al. (J Graph Theory 44:166–177, 2003). It is...
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Strong Edge Coloring of Outerplane Graphs with Independent Crossings
The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of...
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Self-orthogonal codes from equitable partitions of association schemes
We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method, we construct...
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Degree Bounds for the Chromatic Number
Until the 1940s, coloring theory focused almost exclusively on coloring of maps. However, already in 1879 A. B. Kempe suggested coloring of abstract...
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On Equitable Colorings of Hypergraphs
A two-coloring is said to be equitable if, on the one hand, there are no monochromatic edges (the coloring is regular) and, on the other hand, the...
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Total Equitable List Coloring
An equitable coloring is a proper coloring of a graph such that the sizes of the color classes differ by at most one. A graph G is equitably k -colorab...
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Equitable Coloring of Some Convex Polytope Graphs
A proper coloring of graph G is said to be equitable if the number of element(Vertices) in any two color classes differ by atmost one. In equitable...
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Proportional 2-Choosability with a Bounded Palette
Proportional choosability is a list coloring analogue of equitable coloring. Specifically, a k -assignment L for a graph G associates a list L ( v ) of k ...
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1-planar Graphs without 4-cycles or 5-cycles are 5-colorable
A graph is 1-planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge. A proper vertex k -coloring of a...
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Multicolored Bipartite Ramsey Numbers of Large Cycles
For an integer r ≥ 2 and bipartite graphs H i , where 1≤ i ≤ r the bipartite Ramsey number br ( H 1 , H 2 , …, H r ) is the minimum integer N such that any r -ed...
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Perfect 2-coloring of the quartic graphs with order at most 8
In this paper, we study perfect 2-coloring of the quartic graphs with at most 8 vertices. The problem of the existence of perfect coloring is a...
