scholarly journals The game chromatic number of random graphs

2008 ◽  
Vol 32 (2) ◽  
pp. 223-235 ◽  
Author(s):  
Tom Bohman ◽  
Alan Frieze ◽  
Benny Sudakov
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Game Chromatic Number

scholarly journals The eternal game chromatic number of random graphs

2021 ◽  
Vol 95 ◽  
pp. 103324
Author(s):  
Vojtěch Dvořák ◽  
Rebekah Herrman ◽  
Peter van Hintum
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Game Chromatic Number

scholarly journals The Game Chromatic Number of Dense Random Graphs

10.37236/4391 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Ralph Keusch ◽  
Angelika Steger
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
High Probability ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Game Chromatic Number ◽  
Order Of Magnitude ◽  
Random Structures

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 neighboring vertices get different colors. The first player wins this game if and only if at the end, all vertices are colored. The game chromatic number χg(G) is defined as the smallest k for which the first player has a winning strategy.Recently, Bohman, Frieze and Sudakov [Random Structures and Algorithms 2008] analysed the game chromatic number of random graphs and obtained lower and upper bounds of the same order of magnitude. In this paper we improve existing results and show that with high probability, the game chromatic number χg(Gn,p) of dense random graphs with p ≥ e-o(log n) is asymptotically twice as large as the ordinary chromatic number χ(Gn,p).

scholarly journals On the Game Chromatic Number of Sparse Random Graphs

2013 ◽  
Vol 27 (2) ◽  
pp. 768-790
Author(s):  
Alan Frieze ◽  
Simcha Haber ◽  
Mikhail Lavrov
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Game Chromatic Number

scholarly journals Relaxed game chromatic number of trees and outerplanar graphs

2004 ◽  
Vol 281 (1-3) ◽  
pp. 209-219 ◽  
Author(s):  
Wenjie He ◽  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

On the Chromatic Number of Random Graphs

2007 ◽  
pp. 777-788 ◽  
Author(s):  
Amin Coja-Oghlan ◽  
Konstantinos Panagiotou ◽  
Angelika Steger
Keyword(s):  
Chromatic Number ◽  
Random Graphs

scholarly journals On Komlós’ tiling theorem in random graphs

2019 ◽  
Vol 29 (1) ◽  
pp. 113-127
Author(s):  
Rajko Nenadov ◽  
Nemanja Škorić
Keyword(s):  
Chromatic Number ◽  
Random Graph ◽  
Random Graphs ◽  
Upper Bound ◽  
Minimum Degree ◽  
Arbitrary Graph ◽  
Spanning Subgraph ◽  
Delta G ◽  
Image Position ◽  
Vertex Disjoint

AbstractGiven graphs G and H, a family of vertex-disjoint copies of H in G is called an H-tiling. Conlon, Gowers, Samotij and Schacht showed that for a given graph H and a constant γ>0, there exists C>0 such that if $p \ge C{n^{ - 1/{m_2}(H)}}$ , then asymptotically almost surely every spanning subgraph G of the random graph 𝒢(n, p) with minimum degree at least $\delta (G) \ge (1 - \frac{1}{{{\chi _{{\rm{cr}}}}(H)}} + \gamma )np$ contains an H-tiling that covers all but at most γn vertices. Here, χcr(H) denotes the critical chromatic number, a parameter introduced by Komlós, and m2(H) is the 2-density of H. We show that this theorem can be bootstrapped to obtain an H-tiling covering all but at most $\gamma {(C/p)^{{m_2}(H)}}$ vertices, which is strictly smaller when $p \ge C{n^{ - 1/{m_2}(H)}}$ . In the case where H = K3, this answers the question of Balogh, Lee and Samotij. Furthermore, for an arbitrary graph H we give an upper bound on p for which some leftover is unavoidable and a bound on the size of a largest H -tiling for p below this value.

scholarly journals The set chromatic number of random graphs

2016 ◽  
Vol 215 ◽  
pp. 61-70 ◽  
Author(s):  
Andrzej Dudek ◽  
Dieter Mitsche ◽  
Paweł Prałat
Keyword(s):  
Chromatic Number ◽  
Random Graphs

On the game chromatic number of splitting graphs of path and cycle

2019 ◽  
Vol 795 ◽  
pp. 50-56 ◽  
Author(s):  
Muhammad S. Akhtar ◽  
Usman Ali ◽  
Ghulam Abbas ◽  
Mutahira Batool
Keyword(s):  
Chromatic Number ◽  
Game Chromatic Number
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