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A Class of Three-Colorable Triangle-Free Graphs


  • Partially supported by Serbian Ministry for Education and Science grants III44006 and 174033, Serbian-French Technology Co-Operation grant Pavle Savić 2010-2011, and EPSRC grant EP/H021426/1.


The chromatic number of a triangle-free graph can be arbitrarily large. In this article, we show that if all subdivisions of K2, 3 are also excluded as induced subgraphs, then the chromatic number becomes bounded by 3. We give a structural characterization of this class of graphs, from which we derive an inline image coloring algorithm, where n denotes the number of vertices and m the number of edges of the input graph.