Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles

Complexity of Disjoint Π-Vertex Deletion for Disconnected Forbidden Subgraphs

We investigate the computational complexity of Disjoint Π-Vertex Deletion. Here, given an input graph G = (V,E) and a vertex set S ⊆ V , called a solution set, whose removal results in a graph satisfying a non-trivial, hereditary property Π , we are asked to find a solution set S′ with |S′| < |S| and S′∩S = ∅. This problem is partially motivated by the “compression task” occurring in the iterat...

Forbidden Subgraphs and Pancyclicity

We prove that every 2{connected K 1;3-free and Z 3 ?free graph is hamiltonian except for two graphs. Furthermore, we give a complete characterization of all 2?connected, K 1;3-free graphs, which are not pancyclic, and which are Z 3-free, B-free, W-free, or HP 7 ?free.

Hamilton cycles in random subgraphs of pseudo-random graphs

Graphs with Forbidden Subgraphs

Many graphs which are encountered in the study of graph theory are characterized by a type of configuration or subgraph they possess. However, there are occasions when such graphs are more easily defined or described by the kind of subgraphs they are not permitted to contain. For example, a tree can be defined as a connected graph which contains no cycles, and Kuratowski [22] characterized plan...

Forbidden Subgraphs and Cycle Extendability

A graph G on n vertices is pancyclic if G contains cycles of all lengths`for 3 ` n and G is cycle extendable if for every nonhamiltonian cycle C G there is a cycle C 0 G such that V (C) V (C 0) and jV (C 0) n V (C)j = 1. We prove that (i) every 2-connected K 1;3-free graph is pancyclic, if G is P 5-free and n 6, if G is P 6-free and n 10, or if G is P 7-free, deer-free and n 14, and (ii) every ...