@book{1a4506f74af742d98afb9b40a0431a12,

title = "Forbidden subgraphs that imply Hamiltonian-connectedness",

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 $L\in\cal{L}$.",

keywords = "MSC-05C45, MSC-05C35, EWI-3301, IR-65670, MSC-05C38",

author = "Broersma, {Haitze J.} and R.J. Faudree and A. Huck and H. Trommel and H.J. Veldman",

note = "Imported from MEMORANDA",

year = "1999",

language = "Undefined",

series = "Memorandum / Faculty of Mathematical Sciences",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1481",

}