Vertex-Disjoint Cycles of the Same Length
نویسنده
چکیده
Corradi and Hajnal proved that a graph of order at least 3k and minimum degree at least 2k contains k vertex-disjoint cycles. Häggkvist subsequently conjectured that a sufficiently large graph of minimum degree at least four contains two vertex-disjoint cycles of the same length. We prove that this conjecture is correct. In doing so, we give a short proof of the known result that if k > 2, there is an integer nk such that any graph of order at least nk and minimum degree at least 2k contains k vertex-disjoint cycles of the same length.
منابع مشابه
Vertex Disjoint Cycles of the Same Length
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, Cambridge United Kingdom E-mail: [email protected] Corradi and Hajnal proved that a graph of order at least 3k and minimum degree at least 2k contains k vertex-disjoint cycles. Häggkvist subsequently conjectured that a sufficiently large graph of minimum degree at least four contains two vertex-d...
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 66 شماره
صفحات -
تاریخ انتشار 1996