The Guessing Number of Undirected Graphs

  • Demetres Christofides
  • Klas Markström
DOI: https://doi.org/10.37236/679

Abstract

Riis [Electron. J. Combin., 14(1):R44, 2007] introduced a guessing game for graphs which is equivalent to finding protocols for network coding. In this paper we prove upper and lower bounds for the winning probability of the guessing game on undirected graphs. We find optimal bounds for perfect graphs and minimally imperfect graphs, and present a conjecture relating the exact value for all graphs to the fractional chromatic number.

Published
2011-09-26
Issue
Volume 18, Issue 1 (2011)
Article Number
P192