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The Hamilton–Waterloo Problem for ‐Factors and ‐Factors
Authors:Li Wang  Fen Chen  Haitao Cao
Affiliation:Institute of Mathematics, Nanjing Normal University, Nanjing, China
Abstract:The Hamilton–Waterloo problem asks for a 2‐factorization of urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0006 (for v odd) or urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0007 minus a 1‐factor (for v even) into urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0008‐factors and urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0009‐factors. We completely solve the Hamilton–Waterloo problem in the case of C3‐factors and urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0010‐factors for urn:x-wiley:10638539:media:jcd21561:jcd21561-math-0011.
Keywords:Hamilton‐Waterloo problem  cycle decomposition  2‐factorization
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