Abstract.
A 4-uniform hypergraph represents the P 4-structure of a graph G if its hyperedges are the vertex sets of the P 4's in G. By using the weighted 2-section graph of the hypergraph we propose a simple efficient algorithm to decide whether a given 4-uniform hypergraph represents the P 4-structure of a bipartite graph without 4-cycle and 6-cycle. For trees, our algorithm is different from that given by G. Ding and has a better running time namely O(n 2) where n is the number of vertices.
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Revised: February 18, 1998
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Brandstädt, A., Le, V. & Olariu, S. Efficiently Recognizing the P 4-Structure of Trees and of Bipartite Graphs Without Short Cycles. Graphs Comb 16, 381–387 (2000). https://doi.org/10.1007/s003730070002
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DOI: https://doi.org/10.1007/s003730070002