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

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

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.

Injective edge coloring of sparse graphs

2018 ◽  
Vol 10 (02) ◽  
pp. 1850022
Author(s):  
Yuehua Bu ◽  
Chentao Qi
Keyword(s):  
Upper Bound ◽  
Edge Coloring ◽  
Average Degree ◽  
Sparse Graphs ◽  
Maximum Average Degree ◽  
Coloring Number

A [Formula: see text]-injective edge coloring of a graph [Formula: see text] is a coloring [Formula: see text], such that if [Formula: see text], [Formula: see text] and [Formula: see text] are consecutive edges in [Formula: see text], then [Formula: see text]. [Formula: see text] has a [Formula: see text]-injective edge coloring[Formula: see text] is called the injective edge coloring number. In this paper, we consider the upper bound of [Formula: see text] in terms of the maximum average degree mad[Formula: see text], where [Formula: see text].

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

scholarly journals Solving statistical mechanics on sparse graphs with feedback-set variational autoregressive networks

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
Feng Pan ◽  
Pengfei Zhou ◽  
Hai-Jun Zhou ◽  
Pan Zhang
Keyword(s):  
Statistical Mechanics ◽  
Sparse Graphs ◽  
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