On the global strong resilience of fault Hamiltonian graphs

The global strong resilience of G with respect to having a fractional perfect matching, also called FSMP number of G, is the minimum number of edges (or resp., edges and/or vertices) whose deletion results in a graph that has no fractional perfect matchings. A graph G is said to be f-fault Hamiltonian if there exists a Hamiltonian cycle in G - F for any set F of edges and/or vertices with |F | <= f. In this paper, we first give a sufficient condition, involving the independent number, to determine the FSMP number of (delta - 2)-fault Hamiltonian graphs with minimum degree delta >= 2 , and then we can derive the FSMP number of some networks, which generalize some known results. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the global strong resilience of having a fractional perfect matching, as well as the FSMP number and properties of fault Hamiltonian graphs.