On the Grundy Number of a Graph

被引：0

作者：

Havet, Frederic ^{[1
]}

Sampaio, Leonardo ^{[1
]}

机构：

[1] UNSA, CNRS, I3S, Projet Mascotte, F-06902 Sophia Antipolis, France

来源：

PARAMETERIZED AND EXACT COMPUTATION | 2010年 / 6478卷

关键词：

Colouring; Online Colouring; Greedy Colouring; NP-completeness; Fixed Parameter Complexity;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The Grundy number of a graph G, denoted by Gamma(G), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm according to some ordering of the vertices of G. Trivially Gamma(G) <= Delta(G) + 1. In this paper, we show that deciding if Gamma(G) <= Delta(G) is NP-complete. We then show that deciding if Gamma(G) >= vertical bar V(G)vertical bar - k is fixed parameter tractable with respect to the parameter k.

引用

页码：170 / 179

页数：10

共 50 条

[41] THE EAVESDROPPING NUMBER OF A GRAPH
Stuart, Jeffrey L.
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2009, 59 (03) : 623 - 636
[42] The detour number of a graph
Chartrand, G
Johns, GL
Zhang, P
UTILITAS MATHEMATICA, 2003, 64 : 97 - 113
[43] On the domination number of a graph
Pruchnewski, A
DISCRETE MATHEMATICS, 2002, 251 (1-3) : 129 - 136
[44] ON THE COP NUMBER OF A GRAPH
BERARDUCCI, A
INTRIGILA, B
ADVANCES IN APPLIED MATHEMATICS, 1993, 14 (04) : 389 - 403
[45] The Steiner number of a graph
Chartrand, G
Zhang, P
DISCRETE MATHEMATICS, 2002, 242 (1-3) : 41 - 54
[46] On the toll number of a graph
Dravec, Tanja
DISCRETE APPLIED MATHEMATICS, 2022, 321 : 250 - 257
[47] The disconnection number of a graph
Gladdines, Helma
van de Vel, Marcel
TOPOLOGY AND ITS APPLICATIONS, 2011, 158 (03) : 424 - 431
[48] The Alcuin Number of a Graph
Csorba, Peter
Hurkens, Cor A. J.
Woeginger, Gerhard J.
ALGORITHMS - ESA 2008, 2008, 5193 : 320 - 331
[49] PRIME NUMBER GRAPH
POMERANCE, C
MATHEMATICS OF COMPUTATION, 1979, 33 (145) : 399 - 408
[50] The Hoffman number of a graph
Teranishi, Y
DISCRETE MATHEMATICS, 2003, 260 (1-3) : 255 - 265

← 1 2 3 4 5 →