The topology of competitively constructed graphs

Alan Frieze; Wesley Pegden

The topology of competitively constructed graphs

Combinatorics 2014-01-23 v2

Authors: Alan Frieze , Wesley Pegden

Abstract

We consider a simple game, the $k$ -regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$ . We show a sharp topological threshold for this game: for the case $k=3$ a player can ensure the resulting graph is planar, while for the case $k=4$ , a player can force the appearance of arbitrarily large clique minors.

Keywords

graph game topological threshold planar graph clique minors competitive construction degree constraint

Cite

@article{arxiv.1312.0964,
  title  = {The topology of competitively constructed graphs},
  author = {Alan Frieze and Wesley Pegden},
  journal= {arXiv preprint arXiv:1312.0964},
  year   = {2014}
}

Comments

9 pages, 2 figures

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