Characterizations of strongly chordal graphs

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Abstract

In this paper we present several characterizations of the class of strongly chordal graphs. These include a forbidden induced subgraph characterization and two characterizations in terms of totally balanced matrices. Another characterization yields a polynomial recognition algorithm. Interest in these graphs arises in several ways. First, the problems of locating minimum weight dominating sets and minimum weight independent dominating sets in strongly chordal graphs with real vertex weights can be solved in polynomial time, whereas each of these problems is NP-hard for chordal graphs. Moreover, every well-described class of graphs for which polynomial algorithms to solve either of these problems have been presented is a subclass of the class of strongly chordal graphs. Second, these graphs have surprisingly nice structural properties and are intimately related to the class of totally balanced matrices. © 1983.

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Farber, M. (1983). Characterizations of strongly chordal graphs. Discrete Mathematics, 43(2–3), 173–189. https://doi.org/10.1016/0012-365X(83)90154-1

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