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Euler tours of maximum girth in K2n+1 and K2n,2n
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2005 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 21, no 1, p. 107-118Article in journal (Refereed) Published
##### Abstract [en]

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, p. 107-118
##### National Category
Engineering and Technology
##### Identifiers
OAI: oai:DiVA.org:liu-45495DiVA, id: diva2:266391
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Oksimets, Natalia

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Cite
Citation style
• apa
• harvard1
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
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• fi-FI
• nn-NO
• nn-NB
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• Other locale
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• text
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