Stability number and f-factors in graphs

We present a new sufficient condition on stability number and toughness of the graph to have an f-factor

On pseudo 2-factors

AbstractWe show that a graph with minimum degree δ, independence number α≥δ and without isolated vertices, possesses a partition by vertex-disjoint cycles and at most α−δ+1 edges or vertices

Even [a,b]-factors in graphs

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph

Minimum survivable graphs with bounded distance increase

International audienceWe study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increases by more than k. In the design of interconnection networks such graphs guarantee good fault-tolerance properties. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We prove that the problem of finding, in a k-self-repairing graph, a spanning k-self-repairing subgraph of minimum size is NP-Hard