@book{8f7bd2c85efc45e3b346d0e2377b14d1,

title = "On factors of 4-connected claw-free graphs",

abstract = "We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4-connected line graph is Hamiltonian, i.e. has a connected 2-factor. Conjecture 2 (Matthews and Sumner): Every 4-connected claw-free graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglass-free graphs, i.e. graphs that do not contain an induced subgraph isomorphic to two triangles meeting in exactly one vertex. Next we show that a weaker form of Conjecture 2 is true, in which the conclusion is replaced by the conclusion that there exists a connected spanning subgraph in which each vertex has degree two or four. Finally we show that Conjecture 1 and 2 are equivalent to seemingly weaker conjectures in which the conclusion is replaced by the conclusion that there exists a spanning subgraph consisting of a bounded number of paths.",

keywords = "MSC-05C38, MSC-05C45, IR-65680, METIS-141295, EWI-3311",

author = "Broersma, {Haitze J.} and M. Kriesell and M. Kriesell and Z. Ryjacek",

note = "Imported from MEMORANDA",

year = "1999",

language = "Undefined",

isbn = "0169-2690",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente",

number = "1491",

address = "Netherlands",

}