The Hamilton—Waterloo problem: The case of triangle‐factors and one Hamilton cycle | Zendy

Dinitz J.H. | Zendy; Ling Alan C.H. | Zendy

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The Hamilton—Waterloo problem: The case of triangle‐factors and one Hamilton cycle

Author(s) -

Dinitz J.H.,

Ling Alan C.H.

Publication year - 2009

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20196

Subject(s) - mathematics , combinatorics , hamiltonian path , factor (programming language) , factorization , algorithm , computer science , graph , programming language

The Hamilton—Waterloo problem is to determine the existence of a 2‐factorization of K 2 n +1 in which r of the 2‐factors are isomorphic to a given 2‐factor R and s of the 2‐factors are isomorphic to a given 2‐factor S , with r + s = n . In this article we consider the case when R is a triangle‐factor, S is a Hamilton cycle and s = 1. We solve the problem completely except for 14 possible exceptions. This solves a major open case from the 2004 article of Horak et al. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 160–176, 2009

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