We study P6-free graphs, i.e., graphs that do not contain an induced path on six vertices. Our main result is a new characterization of this graph class: a graph G is P6-free if an...
A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length for all 3 ≤ ≤ n. Write α(G) for the independence numbe...
In the Survivable Network Design Problem (SNDP) the goal is to find a minimum cost subset of edges that satisfies a given set of pairwise connectivity requirements among the ver...
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n-...
Catherine S. Greenhill, Fred B. Holt, Nicholas C. ...
For a given connected graph G of order n, a routing R in G is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forw...