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Siberian Advances in Mathematics, ISSN 1055-1344, 7/2019, Volume 29, Issue 3, pp. 183 - 189
DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle [12]. Many known upper bounds... 
DP-coloring of a graph | Mathematics, general | Mathematics | list coloring of a graph | edge coloring
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, p. 48
We consider edge-colorings of 3-uniform hypergraphs which is a natural generalization of the problem of edge-colorings of graphs. Various classes of... 
Coloring | Graph coloring | Scheduling
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 266, pp. 200 - 212
This paper deals with the Θ-stabilized colouring game on the n×n rook’s graph, which constitutes a variant of the classical colouring game on finite graphs so... 
Graph colouring game | Partial Latin square | Autotopism
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2019, Volume 35, Issue 1, pp. 33 - 66
Graph edge coloring has a rich theory, many applications and beautiful conjectures, and it is studied not only by mathematicians, but also by computer... 
Mathematics | Engineering Design | Combinatorics | Chromatic index | Adjacency lemma | Edge coloring | 1-PLANAR GRAPHS | REGULAR GRAPHS | AVERAGE DEGREE | SUFFICIENT CONDITION | MAXIMUM DEGREE-7 | MULTIGRAPHS | MATHEMATICS | INDEPENDENCE NUMBER | PLANAR GRAPHS | INDEX | CHROMATIC CRITICAL GRAPHS | Graph coloring
Journal Article
Association for Computing Machinery. Journal of the Association for Computing Machinery, ISSN 0004-5411, 08/2018, Volume 65, Issue 4
We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum... 
Mathematical problems | Coloring | Lower bounds | Algorithms | Sparsity | Randomized algorithms | Graphs | Symmetry
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 08/2019, Volume 55, Issue 1, pp. 153 - 159
Motivated by the Erdos̋‐Faber‐Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper‐edge... 
linear hypergraph | EFL | chromatic index | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Coloring | Graph theory | Upper bounds | Dependence
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2016, Volume 339, Issue 12, pp. 3043 - 3051
A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k-choosable if... 
Girth | Planar graph | List injective coloring | MATHEMATICS | CHROMATIC NUMBER
Journal Article
DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 08/2019, Volume 266, pp. 200 - 212
This paper deals with the Theta-stabilized colouring game on the n x n rook's graph, which constitutes a variant of the classical colouring game on finite... 
ORDER | MATHEMATICS, APPLIED | NUMBER | Partial Latin square | Autotopism | QUASI-GROUPS | AUTOMORPHISMS | Graph colouring game | LATIN SQUARES | Coloring | Graphs | Upper bounds | Games
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2019, Volume 264, pp. 196 - 207
It is known that the legal coloring of the nodes of a given graph can be reduced to a clique search problem. This paper generalizes this result for... 
Conflict graph | Independent set | Coloring the nodes of a hypergraph | Combinatorial optimization | Clique in a uniform hypergraph | MATHEMATICS, APPLIED | Coloring | Graph theory | Searching | Nodes
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2018, Volume 246, pp. 38 - 48
An edge-colored graph G is said to be rainbow connected if between each pair of vertices there exists a path which uses each color at most once. The rainbow... 
Rainbow coloring | Graph algorithms | Rainbow connection number | Treewidth | MATHEMATICS, APPLIED | VERTEX-CONNECTION | WIDTH | ALGORITHMS | HARDNESS | GRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 11/2019, p. 111712
https://doi.org/10.1016/j.disc.2019.111712 The weak $r$-coloring numbers $wcol_r(G)$ of a graph $G$ were introduced by the first two authors as a... 
Mathematics - Combinatorics
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 521 - 535
A graph is (d1,...,dr)‐colorable if its vertex set can be partitioned into r sets V1,...,Vr so that the maximum degree of the graph induced by Vi is at most di... 
improper coloring | graphs on surfaces | discharging | MATHEMATICS | EVERY PLANAR MAP | LIST IMPROPER COLORINGS | PARTITIONS
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 10/2016, Volume 23, Issue 4, p. 4.4
For a family F of geometric objects in the plane, define chi(F) as the least integer l such that the elements of F can be colored with l colors, in such a way... 
MATHEMATICS | MATHEMATICS, APPLIED | CURVE CONTACT GRAPHS | FREE INTERSECTION GRAPHS | PLANE | Distributed, Parallel, and Cluster Computing | Computer Science
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 2010, Volume 100, Issue 3, pp. 347 - 349
A weighting of the edges of a graph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph. In this paper we... 
Irregular graph labellings | MATHEMATICS | Computer science | Universities and colleges
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 4, pp. 2675 - 2702
A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is... 
Worst-case bounds | Conflict-free coloring | Planar graphs | Complexity | complexity | MATHEMATICS, APPLIED | planar graphs | worst-case bounds | REGIONS | EVERY PLANAR MAP | conflict-free coloring
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 11/2017, Volume 127, pp. 14 - 31
Hadwiger's conjecture from 1943 states that for every integer t≥1, every graph either can be t-colored or has a subgraph that can be contracted to the complete... 
Contraction-critical graph | Hadwiger's conjecture | Graph minor | MINIMAL COUNTEREXAMPLES | MATHEMATICS | HADWIGERS CONJECTURE | EXTREMAL FUNCTION
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, p. 304
No proof of the 4-color conjecture reveals why it is true; the goal has not been to go beyond proving the conjecture. The standard approach involves... 
Mathematical problems | Triangulation | Graph coloring | Equivalence | Images | Diamonds | Graphs | Combinatorics | Four color problem
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, p. 98
A rainbow path in an edge coloured graph is a path in which no two edges are coloured the same. A rainbow colouring of a connected graph G is a colouring of... 
Coloring | Applied mathematics | Color | Graphs | Graph theory | Polynomials | Combinatorics | Optimization
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2019, Volume 342, Issue 12, p. 111623
A graph G is called an IC-planar graph if it can be embedded in the plane so that every edge is crossed by at most one other edge and every vertex is incident... 
Acyclic chromatic number | IC-planar graph | 1-planar graph | Acyclic coloring | MATHEMATICS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2018, Volume 237, pp. 109 - 115
Let χΣt(G) and χΣlt(G) be the neighbor sum distinguishing total chromatic and total choice numbers of a graph G, respectively. In this paper, we present some... 
Neighbor sum distinguishing total coloring | Maximum degree | [formula omitted]-degenerate | Coloring number | ℓ-degenerate | MATHEMATICS, APPLIED | COMBINATORIAL NULLSTELLENSATZ | DISTINGUISHING EDGE COLORINGS | DISTINGUISHING INDEX | l-degenerate | MAXIMUM AVERAGE DEGREE | GRAPHS
Journal Article
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