منابع مشابه
Multicoloured Hamilton Cycles
Mi hael Albert, Alan Frieze and Bru e Reed Department of Mathemati s, Carnegie-Mellon University, Pittsburgh, U.S.A.y Submitted: April 25th,1995 A epted May 9th, 1995 Abstra t The edges of the omplete graph Kn are oloured so that no olour appears more than d ne times, where < 1=32 is a onstant. We show that if n is suÆ iently large then there is a Hamiltonian y le in whi h ea h edge is a di ere...
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Given 0 < p < 1, we prove that a pseudo-random graph G with edge density p and sufficiently large order has the following property: Consider any red/blue-colouring of the edges of G and let r denote the proportion of edges which have colour red. Then there is a Hamilton cycle C so that the proportion of red edges of C is close to r. The analogue also holds for perfect matchings instead of Hamil...
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Let the edges of a graph G be coloured so that no colour is used more than k times. We refer to this as a k-bounded colouring. We say that a subset of the edges of G is multicoloured if each edge is of a different colour. We say that the colouring is H-good, if a multicoloured Hamilton cycle exists i.e., one with a multicoloured edge-set. Let ARk = {G : every k-bounded colouring of G is H-good}...
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It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge disjoint Hamilton cycles, [4], [13], [9]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to color the edges online with σ color...
متن کاملEdge Disjoint Hamilton Cycles
In the late 70s, it was shown by Komlós and Szemerédi ([7]) that for p = lnn+ln lnn+c n , the limit probability for G(n, p) to contain a Hamilton cycle equals the limit probability for G(n, p) to have minimum degree at least 2. A few years later, Ajtai, Komlós and Szemerédi ([1]) have shown a hitting time version of this in the G(n,m) model. Say a graph G has property H if it contains bδ(G)/2c ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1995
ISSN: 1077-8926
DOI: 10.37236/1204