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Premium On Sheehan's Conjecture for Graphs with Symmetry
Šajna Mateja,
Wagner Andrew
Publication year2015
Publication title
journal of graph theory
Resource typeJournals
Abstract Sheehan's Conjecture states that every hamiltonian 4‐regular graph possesses a second Hamilton cycle. In this article, we verify Sheehan's Conjecture for 4‐regular graphs of order n whose automorphism group has size at least2 n 5 if either n ¬ ≡ 0 ( modα ) for all α ∈ { 3 , 4 , 5 } , or n = α m for α ∈ { 3 , 4 , 5 } and m is either an odd prime or a power of 2. We also give lower bounds on the size of the automorphism group and degree of a regular hamiltonian graph that guarantee existence of a second Hamilton cycle.
Subject(s)automorphism , automorphism group , combinatorics , conjecture , discrete mathematics , graph , graph automorphism , graph power , hamiltonian (control theory) , hamiltonian path , line graph , mathematical optimization , mathematics , petersen graph , prime (order theory) , prime power , voltage graph
SCImago Journal Rank1.164

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