IJCCGGT 2003: Combinatorial Geometry and Graph Theory pp 123-132

# Regular Factors Containing a Given Hamiltonian Cycle

• Haruhide Matsuda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

## Abstract

Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n + α, where α = 3 for odd k and α = 4 for even k. Then G has a k – factor (i.e. a k – regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k – factor containing a given Hamiltonian cycle.

## Keywords

Minimum Degree Hamiltonian Cycle Disjoint Subset Large Order Span Subgraph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2005

## Authors and Affiliations

• Haruhide Matsuda
• 1
1. 1.Department of General EducationKyushu Tokai UniversityKumamotoJapan

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