The Hamilton—Waterloo problem: The case of triangle‐factors and one Hamilton cycle
Copyright policy )The Hamilton—Waterloo problem: The case of triangle‐factors and one Hamilton cycle
AbstractThe Hamilton—Waterloo problem is to determine the existence of a 2‐factorization of K2n+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
- University of Vermont United States
Eulerian and Hamiltonian graphs, Oberwolfach problem, resolvable design, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), triple system, Hamilton-Waterlo problem, Paths and cycles
Eulerian and Hamiltonian graphs, Oberwolfach problem, resolvable design, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), triple system, Hamilton-Waterlo problem, Paths and cycles
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