Proof of the 1-Factorization and Hamilton Decomposition Conjectures (Memoirs of the American Mathematical Society)

Proof of the 1-Factorization and Hamilton Decomposition Conjectures (Memoirs of the American Mathematical Society)

By: Bela Csaba (author), Allan Lo (author), Daniela Kuhn (author), Deryk Osthus (author), Andrew Treglown (author)Paperback

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Description

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D 2 n/4 1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, '(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D n/2 . Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree n/2. Then G contains at least regeven (n, )/2 (n 2)/8 edge-disjoint Hamilton cycles. Here regeven (n, ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree . (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case = n/2 of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

About Author

Bela Csaba, University of Szeged, Hungary. Daniela Kuhn, University of Birmingham, United Kingdom. Allan Lo, University of Birmingham, United Kingdom. Deryk Osthus, University of Birmingham, United Kingdom. Andrew Treglown, University of Birmingham, United Kingdom.

Contents

Introduction The two cliques case Exceptional systems for the two cliques case The bipartite case Approximate decompositions Bibliography

Product Details

  • ISBN13: 9781470420253
  • Format: Paperback
  • Number Of Pages: 164
  • ID: 9781470420253
  • ISBN10: 1470420252

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