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Information Processing Letters, ISSN 0020-0190, 11/2019, Volume 151, p. 105835
The graph coloring game on a graph G is a two-player game. In the game, the players alternately color an uncolored vertex of G by a color in a given color set... 
Chromatic number | Combinatorial game | Game chromatic number | COMPUTER SCIENCE, INFORMATION SYSTEMS
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2012, Volume 58, Issue 4, pp. 2524 - 2529
The quantum chromatic number of a graph G is sandwiched between its chromatic number and its clique number, which are well-known NP-hard quantities. We... 
Context | quantum mechanics | Quantum entanglement | Games | Color | Vectors | Graph theory | Information theory | quantum entanglement | GRAPH | COMPUTER SCIENCE, INFORMATION SYSTEMS | MINIMUM RANK | ENGINEERING, ELECTRICAL & ELECTRONIC | Fuzzy sets | Set theory | Quantum computing | Research
Journal Article
Discrete Mathematics, ISSN 0012-365X, 05/2019, Volume 342, Issue 5, pp. 1318 - 1324
A seminal result by Nordhaus and Gaddum states that 2n≤χ(G)+χ(G¯)≤n+1 for every graph G of order n, where G¯ is the complement of G and χ is the chromatic... 
Marking game | Coloring game | Nordhaus–Gaddum type inequalities | MATHEMATICS | Nordhaus-Gaddum type inequalities | GRAPHS | Mathematics
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 11/2019, Volume 795, pp. 50 - 56
Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different... 
Splitting graph | Graph | Game chromatic number | COMPUTER SCIENCE, THEORY & METHODS | INDEX
Journal Article
Journal of Discrete Algorithms, ISSN 1570-8667, 03/2015, Volume 31, pp. 14 - 25
The incidence coloring game has been introduced in Andres (2009) [2] as a variation of the ordinary coloring game. The incidence game chromatic number ιg(G) of... 
Incidence game chromatic number | [formula omitted]-decomposable graphs | Incidence coloring game | Arboricity | Incidence coloring | Arboricity (a, d) -decomposable graphs | Computer Science | Discrete Mathematics
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 12/2016, Volume 83, Issue 4, pp. 334 - 339
A coloring of the edges of a graph G is strong if each color class is an induced matching of G. The strong chromatic index of G, denoted by χs′(G), is the... 
strong chromatic index | coloring number | maximum average degree of a graph | line graph | MATHEMATICS | K-DEGENERATE GRAPHS | NUMBER | GAMES
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2017, Volume 33, Issue 1, pp. 203 - 219
Indicated coloring is a graph coloring game in which there are two players jointly coloring the vertices of a graph in such a way that both can see the entire... 
05C75 | Uniquely colorable graphs | Indicated coloring | Mycielski graphs | Color critical graphs | Mathematics | Engineering Design | Combinatorics | MATHEMATICS | P-5 | Coloring | Games | Texts | Strategy | Graphs | Graph theory | Beneficiation | Players
Journal Article
NEW YORK JOURNAL OF MATHEMATICS, ISSN 1076-9803, 2019, Volume 25, pp. 328 - 361
We associate to each synchronous game a *-algebra whose representations determine whether the game has a perfect deterministic strategy, perfect quantum... 
MATHEMATICS | quantum chromatic number | REAL NULLSTELLENSATZ | QUANTUM | CLOSURE | non-local game | Connes' embedding problem
Journal Article
UTILITAS MATHEMATICA, ISSN 0315-3681, 09/2017, Volume 104, pp. 15 - 22
The game chromatic number x(g) is considered for some convex polytope graphs. We find the exact values for the game chromatic number of Cartesian product graph... 
MATHEMATICS, APPLIED | game chromatic number | STATISTICS & PROBABILITY | CARTESIAN PRODUCT GRAPHS | Cartesian product | convex polytope
Journal Article
Journal of Algebra Combinatorics Discrete Structures and Applications, ISSN 2148-838X, 09/2018, Volume 5, Issue 3, pp. 129 - 136
The game chromatic number $\chi_g$ is investigated for Cartesian product $G\square H$ and corona product $G\circ H$ of two graphs $G$ and $H$. The exact values... 
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 8/2019, Volume 38, Issue 2, pp. 456 - 480
Let $$X\in \{A,B\}$$ X ∈ { A , B } and $$Y\in \{A,B,-\}$$ Y ∈ { A , B , - } , where A, B and − denote (player) Alice, (player) Bob and none of the players,... 
Graph coloring game | Game chromatic number | Line graph | Convex and Discrete Geometry | Operations Research/Decision Theory | Tree | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | Game chromatic index | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2009, Volume 157, Issue 9, pp. 1980 - 1987
We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For k... 
Wheel | Incidence coloring number | Game chromatic number | Star | [formula omitted]-degenerate graph | Cycle | Game chromatic index | k-degenerate graph | MATHEMATICS, APPLIED | OUTERPLANAR GRAPHS | INDEX
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 11/2015, Volume 12, Issue 2-3, pp. 216 - 220
In this paper, we determine the exact values of the game chromatic number of lexicographic product of path P with path P , star K and wheel W . Also we give an... 
Lexicographic product | Graphs | Game chromatic number
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 06/2014, Volume 170, pp. 1 - 6
The edge-coloring game on a graph with a given color set is a two-player game, in which Alice and Bob take turns (with Bob allowed to skip) to color an... 
Graph coloring game | Tree | Caterpillar | Game chromatic number | Game chromatic index | MATHEMATICS, APPLIED | NUMBER | GRAPHS
Journal Article
Far East Journal of Mathematical Sciences, ISSN 0972-0871, 10/2016, Volume 100, Issue 7, pp. 1041 - 1054
In this paper, we investigate exact values of the game chromatic numbers of wheel graphs and also of generalized wheel graphs. 
Game coloring | Game chromatic number | Wheel graph | Graphs | Mathematical analysis | Wheels | Games
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 11/2014, Volume 21, Issue 4
Suppose that two players take turns coloring the vertices of a given graph G with k colors. In each move the current player colors a vertex such that... 
Combinatorial games | Random graphs | Game chromatic number | MATHEMATICS | MATHEMATICS, APPLIED | random graphs | combinatorial games | game chromatic number
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2015, Volume 31, Issue 6, pp. 2381 - 2400
In the $$(r,d)$$ ( r , d ) -relaxed colouring game, two players, Alice and Bob alternately colour the vertices of $$G$$ G , using colours from a set... 
Relaxed colouring game | Mathematics | Engineering Design | Combinatorics | Colouring game | 05C15 | MATHEMATICS | OUTERPLANAR GRAPHS | INDEX
Journal Article
Discrete Mathematics and Theoretical Computer Science, ISSN 1462-7264, 2015, Volume 17, Issue 2, pp. 31 - 48
  While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We... 
Forest | Tree | Game chromatic number | Trees | Forests | Mathematics | Computer Science | Discrete Mathematics
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 05/2018, Volume 25, Issue 2
We study the two-player game where Maker and Breaker alternately color the edges of a given graph G with k colors such that adjacent edges never get the same... 
Random strategies | Edge colorings | Games on graphs | Game chromatic index | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 7/2018, Volume 36, Issue 1, pp. 1 - 12
We prove that the game chromatic index of trees of maximum degree 4 with every 4-vertex (degree-four vertex) being adjacent to at most one 4-vertex does not... 
Graph coloring game | Game chromatic number | Convex and Discrete Geometry | Operations Research/Decision Theory | Tree | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | Game chromatic index | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
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