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Path-Bicolorable Graphs

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Abstract

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 P k -bicolorable if its vertex set V can be partitioned into two subsets (i.e., color classes) V 1 and V 2 such that for every induced P k (a path with exactly k − 1 edges and k vertices) in G, the two colors alternate along the P k , i.e., no two consecutive vertices of the P k belong to the same color class V i , i = 1, 2. Obviously, a graph is bipartite if and only if it is P 2-bicolorable. We give a structural characterization of P 3-bicolorable graphs which also implies linear time recognition of these graphs. Moreover, we give a characterization of P 4-bicolorable graphs in terms of forbidden subgraphs.

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Authors and Affiliations

  1. Institut für Informatik, Universität Rostock, 18051, Rostock, Germany

    Andreas Brandstädt & Van Bang Le

  2. Caesarea Rothschild Institute and Department of Computer Science, University of Haifa, Haifa, Israel

    Martin Charles Golumbic & Marina Lipshteyn

Authors
  1. Andreas Brandstädt
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  2. Martin Charles Golumbic
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  3. Van Bang Le
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  4. Marina Lipshteyn
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Correspondence to Van Bang Le.

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Brandstädt, A., Golumbic, M.C., Le, V.B. et al. Path-Bicolorable Graphs. Graphs and Combinatorics 27, 799–819 (2011). https://doi.org/10.1007/s00373-010-1007-9

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  • DOI: https://doi.org/10.1007/s00373-010-1007-9

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