Orderings on Graphs and Game Coloring Number

Order ◽  
2003 ◽  
Vol 20 (3) ◽  
pp. 255-264 ◽  
Author(s):  
H. A. Kierstead ◽  
Daqing Yang
Keyword(s):  
Coloring Number ◽  
Game Coloring Number

scholarly journals Decomposition of sparse graphs, with application to game coloring number

2010 ◽  
Vol 310 (10-11) ◽  
pp. 1520-1523 ◽  
Author(s):  
Mickael Montassier ◽  
Arnaud Pêcher ◽  
André Raspaud ◽  
Douglas B. West ◽  
Xuding Zhu
Keyword(s):  
Sparse Graphs ◽  
Coloring Number ◽  
Game Coloring Number

The Game Coloring Number of Planar Graphs with a Specific Girth

2018 ◽  
Vol 34 (2) ◽  
pp. 349-354 ◽  
Author(s):  
Keaitsuda Maneeruk Nakprasit ◽  
Kittikorn Nakprasit
Keyword(s):  
Planar Graphs ◽  
Coloring Number ◽  
Game Coloring Number

scholarly journals Game Chromatic Number of Cartesian Product Graphs

10.37236/796 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
T. Bartnicki ◽  
B. Brešar ◽  
J. Grytczuk ◽  
M. Kovše ◽  
Z. Miechowicz ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Cartesian Product ◽  
Chromatic Numbers ◽  
Cartesian Products ◽  
Game Chromatic Number ◽  
Coloring Number ◽  
Product Graphs ◽  
Complete Bipartite Graphs ◽  
Game Coloring Number ◽  
Product Of Graphs

The game chromatic number $\chi _{g}$ is considered for the Cartesian product $G\,\square \,H$ of two graphs $G$ and $H$. Exact values of $\chi _{g}(K_2\square H)$ are determined when $H$ is a path, a cycle, or a complete graph. By using a newly introduced "game of combinations" we show that the game chromatic number is not bounded in the class of Cartesian products of two complete bipartite graphs. This result implies that the game chromatic number $\chi_{g}(G\square H)$ is not bounded from above by a function of game chromatic numbers of graphs $G$ and $H$. An analogous result is derived for the game coloring number of the Cartesian product of graphs.

A NOTE ON THE SHADOW COCYCLE INVARIANT OF A KNOT WITH A BASE POINT

2007 ◽  
Vol 16 (07) ◽  
pp. 959-967 ◽  
Author(s):  
S. SATOH
Keyword(s):  
Base Point ◽  
Laurent Polynomials ◽  
Coloring Number

Fox's shadow p-colorings of a knot K define two kinds of Laurent polynomials, Φp(K) and [Formula: see text], as invariants of K. We prove that the equality [Formula: see text] holds for any knot K. Also we prove that, if the p-coloring number of K is equal to p2, then [Formula: see text] has the form [Formula: see text] for some N ∈ ℤp.

scholarly journals The irregular coloring number of a tree

1995 ◽  
Vol 141 (1-3) ◽  
pp. 279-283 ◽  
Author(s):  
Anita C. Burris
Keyword(s):  
Coloring Number

Note on a new coloring number of a graph

1980 ◽  
Vol 4 (1) ◽  
pp. 111-113 ◽  
Author(s):  
P. Horák ◽  
J. Širáň
Keyword(s):  
Coloring Number
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