On factors of 4connected clawfree graphs
Broersma, H.J. and Kriesell, M. and Ryjacek, Z. (1999) On factors of 4connected clawfree graphs. [Report]

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Abstract:  We consider the existence of several different kinds of factors in 4connected clawfree 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 4connected line graph is Hamiltonian, i.e. has a connected 2factor. Conjecture 2 (Matthews and Sumner): Every 4connected clawfree graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglassfree 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.

Item Type:  Report 
Additional information:  Imported from MEMORANDA 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/65680 
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