Results 21 to 30 of about 4,036,327 (265)
A sharp threshold for the Hamilton cycle Maker–Breaker game
Random Structures and Algorithms, 2009 Dan Hefetz +3 more
semanticscholar +3 more sources
Multicoloured Hamilton Cycles [PDF]
The Electronic Journal of Combinatorics, 1995 The edges of the complete graph $K_n$ are coloured so that no colour appears more than $\lceil cn\rceil$ times, where $c < 1/32$ is a constant. We show that if $n$ is sufficiently large then there is a Hamiltonian cycle in which each edge is a different colour, thereby proving a 1986 conjecture of Hahn and Thomassen. We prove a similar result for
Albert, Michael +2 more
openaire +2 more sources
Triangle resilience of the square of a Hamilton cycle in random graphs [PDF]
J. Comb. Theory B, 2018 Since first introduced by Sudakov and Vu in 2008, the study of resilience problems in random graphs received a lot of attention in probabilistic combinatorics. Of particular interest are resilience problems of spanning structures.
Manuela Fischer +3 more
semanticscholar +1 more source
Finding a Hamilton cycle fast on average using rotations and extensions [PDF]
Random Struct. Algorithms, 2019 We present an algorithm CRE, which either finds a Hamilton cycle in a graph G or determines that there is no such cycle in the graph. The algorithm's expected running time over input distribution G∼G(n,p) is (1+o(1))n/p, the optimal possible expected ...
Yahav Alon, Michael Krivelevich
semanticscholar +1 more source
On Hamilton cycle decompositions of the tensor product of complete graphs
Discrete Mathematics, 2003 R. Balakrishnan +3 more
semanticscholar +3 more sources
Packing Hamilton Cycles Online [PDF]
Combinatorics, Probability and Computing, 2018 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, 9, 13]. 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.
Briggs, Joseph +4 more
openaire +4 more sources
Resilience for loose Hamilton cycles
Procedia Computer Science, 2023 We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum $d$-degree threshold for loose Hamiltonicity relative to the random $k$-uniform hypergraph $H_k(n,p)$ coincides with its dense analogue whenever $p \geq n^{- (k-1)/2+o(1)}$.
Alvarado, José D. +4 more
openaire +2 more sources
Packing Loose Hamilton Cycles [PDF]
Combinatorics, Probability and Computing, 2017 A subsetCof edges in ak-uniform hypergraphHis aloose Hamilton cycleifCcovers all the vertices ofHand there exists a cyclic ordering of these vertices such that the edges inCare segments of that order and such that every two consecutive edges share exactly one vertex.
Ferber, Asaf +3 more
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Extending Cycles Locally to Hamilton Cycles [PDF]
The Electronic Journal of Combinatorics, 2016 A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle $S^1$ that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs.
Hamann, Matthias +2 more
openaire +2 more sources