Results 11 to 20 of about 2,293,482 (304)
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 $p \geq n^{- (k-1)/2+o(1)}$.
José D. Alvarado +4 more
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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
Michael H. Albert +2 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.
Matthias Hamann +2 more
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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
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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.
Asaf Ferber +3 more
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Discrete Mathematics, 1993 If the complete graph on \(n\) vertices is edge-colored such that the number of times that a color may occur is less than \(cn/\log(n)\), where \(c\) is a fixed constant, then there is a Hamiltonian cycle in which no two edges have the same color.
Alan M. Frieze, Bruce A. Reed
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Oriented discrepancy of Hamilton cycles
Journal of Graph Theory, 2023 AbstractWe propose the following extension of Dirac's theorem: if is a graph with vertices and minimum degree , then in every orientation of there is a Hamilton cycle with at least edges oriented in the same direction. We prove an approximate version of this conjecture, showing that minimum degree guarantees a Hamilton cycle with at least edges ...
Lior Gishboliner +2 more
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Hamilton cycles in quasirandom hypergraphs [PDF]
Random Structures & Algorithms, 2016 We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $Ω(n^{k-1})$ contains a loose Hamilton cycle. We also give a construction to show that a $k$-uniform hypergraph satisfying these conditions need not contain a ...
John Lenz, Dhruv Mubayi, Richard Mycroft
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Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
Discussiones Mathematicae Graph Theory, 2013 Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2.
Chitra V., Muthusamy A.
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Hamilton-connected properties in cartesian product [PDF]
Transactions on Combinatorics, 2012 In this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. We present some sufficient and necessary conditions for $GBox H$ being hamilton-connected when $G$ is a hamilton-connected ...
Rushengul Hoshur, Elkin Vumar
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