Euler tours of maximum girth in K2n+1 and K2n,2n
2005 (English)In: Graphs and Combinatorics, ISSN 0911-0119, Vol. 21, no 1, 107-118 p.Article in journal (Refereed) Published
Given an eulerian graph G and an Euler tour T of G, the girth of T, denoted by g(T), is the minimum integer k such that some segment of k+1 consecutive vertices of T is a cycle of length k in G. Let g E (G)= maxg(T) where the maximum is taken over all Euler tours of G. We prove that g E (K 2n,2n )=4n-4 and 2n-3=g E (K 2n+1)=2n-1 for any n=2. We also show that g E (K 7)=4. We use these results to prove the following: 1)The graph K 2n,2n can be decomposed into edge disjoint paths of length k if and only if k=4n-1 and the number of edges in K 2n,2n is divisible by k. 2)The graph K 2n+1 can be decomposed into edge disjoint paths of length k if and only if k=2n and the number edges in K 2n+1 is divisible by k. © Springer-Verlag 2005.
Place, publisher, year, edition, pages
2005. Vol. 21, no 1, 107-118 p.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-45495DOI: 10.1007/s00373-004-0578-8OAI: oai:DiVA.org:liu-45495DiVA: diva2:266391