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Journal of Graph Theory, ISSN 0364-9024, 11/2019, Volume 92, Issue 3, pp. 191 - 206
Let G be a graph with a list assignment L. Suppose a preferred color is given for some of the vertices; how many of these preferences can be respected when... 
constraint satisfaction | combinatorial nullstellensatz | list coloring | MATHEMATICS
Journal Article
Fullerenes, Nanotubes and Carbon Nanostructures, ISSN 1536-383X, 11/2018, Volume 26, Issue 11, pp. 705 - 708
A (k,6)-fullerene graph is a planar 3-connected cubic graph whose faces are k-gons and hexagons. The aim of this paper is to compute the equitable chromatic,... 
equitable coloring | b-coloring | list coloring | (k,6)-fullerene | graph operations | MATERIALS SCIENCE, MULTIDISCIPLINARY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | NANOSCIENCE & NANOTECHNOLOGY
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2018, Volume 34, Issue 6, pp. 1637 - 1649
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-colorable if... 
Total coloring | List coloring | Graph coloring | Equitable choosability | Equitable coloring | MATHEMATICS | TOTAL CHOOSABILITY | PLANAR GRAPHS | EDGE | Coloring | Graph theory | Apexes | Color
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 222, pp. 166 - 171
For positive integers k and r, a (k,r)-coloring of a graph G is a proper coloring of the vertices with k colors such that every vertex of degree i will be... 
List r-dynamic coloring | r-dynamic coloring | Claw-free
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2018, Volume 87, Issue 4, pp. 492 - 508
The dichromatic number χ⃗(D) of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an... 
digraphs | list coloring | dichromatic number | list dichromatic number | MATHEMATICS | NUMBER | Computer Science | Discrete Mathematics
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2019, Volume 363, p. 124562
Let G be a maximal plane graph of diameter at most two. Let χl(G) and χd(G) denote the list chromatic number and the diagonal chromatic number of G,... 
List coloring | Plane graph of diameter two | Diagonal coloring | MATHEMATICS, APPLIED | EDGE CHOOSABILITY
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 03/2016, Volume 81, Issue 3, pp. 272 - 282
We prove that the list chromatic index of a graph of maximum degree Δ and treewidth ≤2Δ−3 is Δ; and that the total chromatic number of a graph of maximum... 
list colouring | tree width | total colouring | MULTIGRAPH | MATHEMATICS | TOTAL CHROMATIC NUMBER
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 07/2019, Volume 54, Issue 4, pp. 653 - 664
The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for... 
entropy compression | Graph coloring | Local Lemma | list coloring | DP‐coloring | triangle‐free graphs | triangle-free graphs | DP-coloring | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | GRAPHS | Coloring | Mathematics - Combinatorics
Journal Article
Combinatorica, ISSN 0209-9683, 12/2016, Volume 36, Issue 6, pp. 661 - 686
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the same sequence of colours as the second half. A graph is... 
Mathematics, general | Mathematics | Combinatorics | 05C15 | MATHEMATICS | ACYCLIC COLORINGS | TREES | SEQUENCES | LOVASZ | STAR | VERTEX COLORINGS | PLANAR GRAPHS | LOCAL LEMMA | Computer science | Electrical engineering
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2013, Volume 161, Issue 13-14, pp. 2207 - 2212
A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two... 
Dynamic coloring | Four color theorem | Dynamic chromatic number | Planar graph | MATHEMATICS, APPLIED | MAP | Coloring | Graphs | Lists | Dynamics | Mathematical analysis
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 03/2018, Volume 129, pp. 38 - 54
We introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible... 
Correspondence coloring | List coloring | Planar graphs | DP-coloring | MATHEMATICS
Journal Article
Annals of Operations Research, ISSN 0254-5330, 7/2009, Volume 169, Issue 1, pp. 3 - 16
Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the... 
Coloring | Operations Research/Decision Theory | Theory of Computation | Combinatorics | List-coloring | Computational complexity | Economics / Management Science | INTERVAL-GRAPHS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRECOLORING EXTENSION | Studies | Operations research | Mathematical models | Mathematics | Graph coloring | Statistical analysis
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 2018, Volume 1
Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has... 
MONOCHROMATIC COMPONENTS | MATHEMATICS | MATHEMATICS, APPLIED | SEPARATOR THEOREM | MAXIMUM DEGREE | EVERY PLANAR GRAPH | LIST IMPROPER COLORINGS | CHROMATIC NUMBER | LIGHT SUBGRAPHS | SPARSE GRAPHS | EXTREMAL FUNCTION | VERTEX PARTITIONS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2016, Volume 32, Issue 4, pp. 1635 - 1640
A sequence $$a_1a_2\ldots a_p$$ a 1 a 2 … a p is an r-repetition (for a real number $$r >1 $$ r > 1 ) if $$p=\lceil rq \rceil $$ p = ⌈ r q ⌉ for some positive... 
Path | Non-repetitive chromatic number | Mathematics | Engineering Design | Combinatorics | Non-repetitive list colouring | Entropy method | MATHEMATICS | WORDS | DEJEANS CONJECTURE | PROOF | Integers | Color | Texts | Graphs | Colouring | Graph theory | Combinatorial analysis | Colour
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 267, pp. 73 - 84
Let G be a graph and P be a class of graphs. We consider list colouring of vertices of G in which the sizes of lists assigned to different vertices can be... 
Hereditary classes of graphs | 2-trees | Sum-list colouring | MATHEMATICS, APPLIED | Algorithms | Coloring | Apexes | Upper bounds | Lists | Color | Graphs | Trees (mathematics) | Graph theory | Polynomials
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
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
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
Information Processing Letters, ISSN 0020-0190, 2011, Volume 111, Issue 11, pp. 538 - 540
Motivated by reliability considerations in data deduplication for storage systems, we introduce the problem of flexible coloring. Given a hypergraph H and the... 
Approximation algorithms | Graph coloring | Graph algorithms | Hardness of approximation | COMPUTER SCIENCE, INFORMATION SYSTEMS | Hardness | Analysis | Algorithms | Coloring | Approximation | Lists | Mathematical analysis | Storage systems | Images | Counting
Journal Article
IEEE Transactions on Evolutionary Computation, ISSN 1089-778X, 12/2019, Volume 23, Issue 6, pp. 1015 - 1028
Journal Article
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