Connected, bounded degree, triangle avoidance games
The electronic journal of combinatorics, Tome 18 (2011) no. 1
We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on $n$ vertices. The two players take turns choosing edges within $K_{n}$, building up a simple graph. The edges must be chosen according to a set of restrictions $\mathcal{R}$. The winner is the last player to choose an edge that does not violate any of the restrictions in $\mathcal{R}$. For fixed $n$ and $\mathcal{R}$, one of the players has a winning strategy. For a pair of games where $\mathcal{R}$ includes bounded degree, connectedness, and triangle-avoidance, we determine the winner for all values of $n$.
@article{10_37236_680,
author = {Nishali Mehta and \'Akos Seress},
title = {Connected, bounded degree, triangle avoidance games},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/680},
zbl = {1229.05210},
url = {http://geodesic.mathdoc.fr/articles/10.37236/680/}
}
Nishali Mehta; Ákos Seress. Connected, bounded degree, triangle avoidance games. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/680
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