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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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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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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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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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On Equitable Near Proper Coloring of Mycielski Graph of Graphs
When the available number of colors are less than that of the equitable chromatic number, there may be some edges whose end vertices receive the same...
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A new distributed graph coloring algorithm for large graphs
The vertex graph coloring problem (VGCP) is one of the most well-known problems in graph theory. It is used for solving several real-world problems...
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Structural Parameterizations of Budgeted Graph Coloring
We introduce a variant of the graph coloring problem, which we denote as Budgeted Coloring Problem (BCP). Given a graph G, an integer c and an...
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Structural Parameterizations for Equitable Coloring
An n-vertex graph is equitably k-colorable if there is a proper coloring of its vertices such that each color is used either $$\left\lfloor...
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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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LCD codes from equitable partitions of association schemes
Linear codes with complementary duals (shortly named LCD codes) are linear codes whose intersection with their duals are trivial. In this paper, we...
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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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Complexity of Tree-Coloring Interval Graphs Equitably
An equitable tree-k-coloring of a graph is a vertex k-coloring such that each color class induces a forest and the size of any two color classes...
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Total chromatic number for some classes of Cayley graphs
In this paper, we have obtained the total chromatic number for some classes of Cayley graphs, particularly the Unitary Cayley graphs on even order...