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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 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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The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets
This paper deals with list colorings of uniform hypergraphs. Let H ( m, r, k ) be the complete r -partite k -uniform hypergraph with parts of equal size m ...
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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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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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On the Universality and Extremality of Graphs with a Distance Constrained Colouring
A lambda colouring (or L (2, 1)-colouring) of a graph is an assignment of non-negative integers (with minimum assignment 0) to its vertices such that...
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Sharp Bounds on the Aα-index of Graphs in Terms of the Independence Number
Given a graph G , the adjacency matrix and degree diagonal matrix of G are denoted by A ( G ) and D ( G ), respectively. In 2017, Nikiforov [24] proposed the A
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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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Fractional Matchings, Component-Factors and Edge-Chromatic Critical Graphs
The first part of the paper studies star-cycle factors of graphs. It characterizes star-cycle factors of a graph G and proves upper bounds for the...
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Regularity Lemma and van der Waerden Number
Bartel L. van der Waerden (February 2, 1903–January 12, 1996) was a Dutch mathematician, who published his Algebra, an influential two-volume...
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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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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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Proportional Choosability of Complete Bipartite Graphs
Proportional choosability is a list analogue of equitable coloring that was introduced in 2019. The smallest k for which a graph G is proportionally k ...
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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 ...