Uniqueness of maximal dominating cycles in 3‐regular graphs and of hamiltonian cycles in 4‐regular graphs | Zendy

Fleischner Herbert | Zendy

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

Author(s) -

Fleischner Herbert

Publication year - 1994

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190180503

Subject(s) - mathematics , eulerian path , cycle basis , combinatorics , uniqueness , hamiltonian path , pancyclic graph , hamiltonian (control theory) , indifference graph , discrete mathematics , chordal graph , graph , 1 planar graph , pure mathematics , line graph , graph power , lagrangian , mathematical analysis , mathematical optimization

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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