Forbidden subgraphs that imply Hamiltonian-connectedness


Broersma, H.J. and Faudree, R.J. and Huck, A. and Trommel, H. and Veldman, H.J. (1999) Forbidden subgraphs that imply Hamiltonian-connectedness. [Report]

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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 $L\in\cal{L}$.
Item Type:Report
Copyright:© 1999 University of Twente, Faculty of Mathematical Sciences
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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