Hereditary modular graphs

Abstract

In a hereditary modular graphG, for any three verticesu, v, w of an isometric subgraph ofG, there exists a vertex of this subgraph that is simultaneously on some shortestu, v-path,u, w-path andv, w-path. It is shown that the hereditary modular graphs are precisely those bipartite graphs which do not contain any isometric cycle of length greater than four. There is a polynomial-time algorithm available which decides whether a given (bipartite) graph is hereditary modular or not. Finally, the chordal bipartite graphs are characterized by forbidden isometric subgraphs.

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Bandelt, H.J. Hereditary modular graphs. Combinatorica 8, 149–157 (1988). https://doi.org/10.1007/BF02122796

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AMS subject classification (1980)

  • 05C38