# Forbidden subgraphs that imply Hamiltonian-connectedness

Haitze J. Broersma, R.J. Faudree, A. Huck, H. Trommel, H.J. Veldman

Research output: Book/ReportReportOther research output

## Abstract

It is proven that if $G$ is a $3$-connected claw-free graph which is also $Z_3$-free (where $Z_3$ is a triangle with a path of length $3$ attached), $P_6$-free (where $P_6$ is a path with $6$ vertices) or $H_1$-free (where $H_1$ consists of two disjoint triangles connected by an edge), then $G$ is Hamiltonian-connected. Also, examples will be described that determine a finite family of graphs $\cal{L}$ such that if a 3-connected graph being claw-free and $L$-free implies $G$ is Hamiltonian-connected, then $L\in\cal{L}$.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics Published - 1999

### Publication series

Name Memorandum / Faculty of Mathematical Sciences Department of Applied Mathematics, University of Twente 1481 0169-2690

• MSC-05C45
• MSC-05C35
• EWI-3301
• IR-65670
• MSC-05C38