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Article Dans Une Revue Contributions to Discrete Mathematics Année : 2011

Claw-freeness, $3$-homogeneous subsets of a graph and a reconstruction problem

Maurice Pouzet
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Hamza Si Kaddour
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Nicolas Trotignon

Résumé

We describe ${\rm Forb}\{K_{1,3}, \overline {K_{1,3}}\}$, the class of graphs $G$ such that $G$ and its complement $ \overline{G}$ are claw-free. With few exceptions, it is made of graphs whose connected components consist of cycles of length at least 4, paths, and of the complements of these graphs. Considering the hypergraph ${\mathcal H} ^{(3)}(G)$ made of the $3$-element subsets of the vertex set of a graph $G$ on which $G$ induces a clique or an independent subset, we deduce from above a description of the Boolean sum $G\dot{+}G'$ of two graphs $G$ and $G'$ giving the same hypergraph. We indicate the role of this latter description in a reconstruction problem of graphs up to complementation.
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Dates et versions

hal-00839758 , version 1 (29-06-2013)

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  • HAL Id : hal-00839758 , version 1

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Maurice Pouzet, Hamza Si Kaddour, Nicolas Trotignon. Claw-freeness, $3$-homogeneous subsets of a graph and a reconstruction problem. Contributions to Discrete Mathematics, 2011, 6, pp.92-103. ⟨hal-00839758⟩
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