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arXiv · 1711.07736

On $P_5$-free Chordal bipartite graphs

S Aadhavan·P Renjith·N Sadagopan
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Abstract

A bipartite graph is chordal bipartite if every cycle of length at least 6 has a chord in it. In this paper, we investigate the structure of $P_5$-free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering, a special ordering among its vertices. Further, using this ordering, we present polynomial-time algorithms for classical problems such as Hamiltonian cycle (path) and longest path. Two variants of Hamiltonian path include Steiner path and minimum leaf spanning tree, and we obtain polynomial-time algorithms for these problems as well restricted to $P_5$-free chordal bipartite graphs.

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S Aadhavan, P Renjith, N Sadagopan. 2017-11-21. On $P_5$-free Chordal bipartite graphs. https://arxiv.org/abs/1711.07736

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