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Uniqueness of maximal dominating cycles in 3-regular graphs and of hamiltonian cycles in 4-regular graphs

✍ Scribed by Herbert Fleischner

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
461 KB
Volume
18
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

We construct 3‐regular (cubic) graphs G that have a dominating cycle C such that no other cycle C~1~ of G satisfies V(C) ⊆ V(C~1~). By a similar construction we obtain loopless 4‐regular graphs having precisely one hamiltonian cycle. The basis for these constructions are considerations on the uniqueness of a cycle decomposition compatible with a given eulerian trail in some eulerian graph.

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