Braodcast Chromatic Numbers of Graphs

@article{Goddard2008BraodcastCN,
  title={Braodcast Chromatic Numbers of Graphs},
  author={Wayne Goddard and Sandra Mitchell Hedetniemi and Stephen T. Hedetniemi and John M. Harris and Douglas F. Rall},
  journal={Ars Comb.},
  year={2008},
  volume={86}
}
A function π : V → {1, . . . , k} is a broadcast coloring of order k if π(u) = π(v) implies that the distance between u and v is more than π(u). The minimum order of a broadcast coloring is called the broadcast chromatic number of G, and is denoted χb(G). In this paper we introduce this coloring and study its properties. In particular, we explore the relationship with the vertex cover and chromatic numbers. While there is a polynomial-time algorithm to determine whether χb(G) ≤ 3, we show that… CONTINUE READING
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