We introduce the concept of a 2-starter in a group G of odd order. We prove that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G. Some classes of 2-starters are studied, with special attention given to those leading to solutions of some Oberwolfach or Hamilton-Waterloo problems.
On sharply vertex transitive 2-factorizations of the complete graph / M., Buratti; Rinaldi, Gloria. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - STAMPA. - 111:2(2005), pp. 245-256. [10.1016/j.jcta.2004.11.014]
On sharply vertex transitive 2-factorizations of the complete graph
RINALDI, Gloria
2005
Abstract
We introduce the concept of a 2-starter in a group G of odd order. We prove that any 2-factorization of the complete graph admitting G as a sharply vertex transitive automorphism group is equivalent to a suitable 2-starter in G. Some classes of 2-starters are studied, with special attention given to those leading to solutions of some Oberwolfach or Hamilton-Waterloo problems.
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