Spanning 3-colourable subgraphs of small bandwidth in dense graphs
نویسندگان
چکیده
A conjecture by Bollobás and Komlós states the following: For every γ > 0 and integers r ≥ 2 and ∆, there exists β > 0 with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least ( r−1 r + γ)n and H is an r-chromatic graph with n vertices, bandwidth at most βn and maximum degree at most ∆, then G contains a copy of H. This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r = 3.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 98 شماره
صفحات -
تاریخ انتشار 2008