scholarly journals The Game Coloring Number of Planar Graphs

1999 ◽  
Vol 75 (2) ◽  
pp. 245-258 ◽  
Author(s):  
Xuding Zhu
Keyword(s):  
Planar 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 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 Two-Coloring Number and Degenerate Colorings of Planar Graphs

2009 ◽  
Vol 23 (3) ◽  
pp. 1548-1560 ◽  
Author(s):  
Hal Kierstead ◽  
Bojan Mohar ◽  
Simon Špacapan ◽  
Daqing Yang ◽  
Xuding Zhu
Keyword(s):  
Planar Graphs ◽  
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.

scholarly journals On the weak 2-coloring number of planar graphs

2022 ◽  
Vol 345 (1) ◽  
pp. 112631
Author(s):  
Ahlam Almulhim ◽  
H.A. Kierstead
Keyword(s):  
Planar Graphs ◽  
Coloring Number

scholarly journals Planar graphs have two-coloring number at most 8

2018 ◽  
Vol 130 ◽  
pp. 144-157 ◽  
Author(s):  
Zdeněk Dvořák ◽  
Adam Kabela ◽  
Tomáš Kaiser
Keyword(s):  
Planar Graphs ◽  
Coloring Number

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line
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