A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost ...

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

Dantas, S.De Figueiredo, CelinaMaffray, FrédéricTeixeira, Rafael B.

The $\Pi$ graph sandwich problem asks, for a pair of graphs$G_1=(V,E_1)$ and $G_2=(V,E_2)$ with $E_1\subseteq E_2$, whether thereexists a graph $G=(V,E)$ that satisfies property $\Pi$ and$E_1\subseteq E \subseteq E_2$. We consider the property of being$F$-free, where $F$ is a fixed graph. We show that the claw-freegraph sandwich and the bull-free g...