## 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.

Original language | English |
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Pages (from-to) | 799-819 |

Number of pages | 21 |

Journal | Graphs and Combinatorics |

Volume | 27 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2011 |

## Keywords

- 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