Path-Bicolorable Graphs

Andreas Brandstädt, Martin Charles Golumbic, Van Bang Le, Marina Lipshteyn

Research output: Contribution to journalArticlepeer-review


In this paper, we introduce the notion of path-bicolorability that generalizes bipartite graphs in a natural way: For k ≥ 2, a graph G = (V, E) is Pk-bicolorable if its vertex set V can be partitioned into two subsets (i. e., color classes) V1 and V2 such that for every induced Pk (a path with exactly k - 1 edges and k vertices) in G, the two colors alternate along the Pk, i. e., no two consecutive vertices of the Pk belong to the same color class Vi, i = 1, 2. Obviously, a graph is bipartite if and only if it is P2-bicolorable. We give a structural characterization of P3-bicolorable graphs which also implies linear time recognition of these graphs. Moreover, we give a characterization of P4-bicolorable graphs in terms of forbidden subgraphs.

Original languageEnglish
Pages (from-to)799-819
Number of pages21
JournalGraphs and Combinatorics
Issue number6
StatePublished - Nov 2011


  • 3-Leaf powers
  • Bipartite graphs
  • Linear time recognition
  • P-Bicolorable graphs
  • P-Bicolorable graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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