Cycles in Hamiltonian graphs of prescribed maximum degree

Authors:
Antoni Marczyk;Mariusz Woźniak
Affiliations:
Faculty of Applied Mathematics A G H, Al. Mickiewicza 30, 30-059 Kraków, Poland;Faculty of Applied Mathematics A G H, Al. Mickiewicza 30, 30-059 Kraków, Poland
Venue:
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Year:
2003

Citing 4
Cited 0

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Abstract

Let G be a Hamiltonian graph G of order n and maximum degree Δ, and let C(G) denote the set of cycle lengths occurring in G. It is easy to see that |C(G)| ≥ Δ - 1. In this paper, we prove that if Δ n/2, then |C(G)| ≥ (n + Δ - 3)/2. We also show that for every Δ ≥ 2 there is a graph G of order n ≥ 2Δ such that |C(G)| = Δ - 1, and the lower bound in case Δ n/2 is best possible.