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Journal Articles The Electronic Journal of Combinatorics Year : 2012

On $({K}\_{q},k)$ stable graphs with small $k$

Abstract

A graph G is (Kq; k) stable if it contains a copy of Kq after deleting any subset of k vertices. In a previous paper we have characterized the (Kq; k) stable graphs with minimum size for 2 < q < 6 and we have proved that the only (Kq; k) stable graph with minimum size is Kq+k for q > 4 and k < 4. We show that for q > 5 and k <= q/2+1 the only (Kq; k) stable graph with minimum size is isomorphic to Kq+k.

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Dates and versions

hal-00934318 , version 1 (29-01-2014)

Identifiers

  • HAL Id : hal-00934318 , version 1

Cite

Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe, Adam Pawel Wojda. On $({K}\_{q},k)$ stable graphs with small $k$. The Electronic Journal of Combinatorics, 2012, 19 (2), pp.#P50. ⟨hal-00934318⟩
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