Cyclability in bipartite graphs

Let $G=(X,Y,E)$ be a balanced $2$-connected bipartite graph and $S \subset V(G)$. We will say that $S$ is cyclable in $G$ if all vertices of $S$ belong to a common cycle in $G$. We give sufficient degree conditions in a balanced bipartite graph $G$ and a subset $S \subset V(G)$ for the cyclability of the set $S$

Removable edges, cycles and connectivity in graphs

ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Cyclability in bipartite graphs

Let $G=(X,Y,E)$ be a balanced $2$-connected bipartite graph and $S \subset V(G)$. We will say that $S$ is cyclable in $G$ if all vertices of $S$ belong to a common cycle in $G$. We give sufficient degree conditions in a balanced bipartite graph $G$ and a subset $S \subset V(G)$ for the cyclability of the set $S$

Factor-criticality and matching extension in DCT-graphs

The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p + 1)-connected DCT-graph G is p-extendable, i.e. every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs

A degree condition implying that every matching is contained in a hamiltonian cycle

AbstractWe give a degree sum condition for three independent vertices under which every matching of a graph lies in a hamiltonian cycle. We also show that the bound for the degree sum is almost the best possible

Sufficient conditions for existence of long cycles in graphs

ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF