Path-Bicolorable Graphs

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

doi:10.1007/s00373-010-1007-9

Path-Bicolorable Graphs

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

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) V₁ and V₂ 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 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 language	English
Pages (from-to)	799-819
Number of pages	21
Journal	Graphs and Combinatorics
Volume	27
Issue number	6
DOIs	https://doi.org/10.1007/s00373-010-1007-9
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

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10.1007/s00373-010-1007-9

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title = "Path-Bicolorable Graphs",

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 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.",

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author = "Andreas Brandst{\"a}dt and Golumbic, {Martin Charles} and Le, {Van Bang} and Marina Lipshteyn",

year = "2011",

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doi = "10.1007/s00373-010-1007-9",

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T1 - Path-Bicolorable Graphs

AU - Brandstädt, Andreas

AU - Golumbic, Martin Charles

AU - Le, Van Bang

AU - Lipshteyn, Marina

PY - 2011/11

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N2 - 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.

AB - 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.

KW - 3-Leaf powers

KW - Bipartite graphs

KW - Linear time recognition

KW - P-Bicolorable graphs

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Path-Bicolorable Graphs

Abstract

Keywords

ASJC Scopus subject areas

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