Results 11 to 20 of about 3,218,251 (319)
Color‐biased Hamilton cycles in random graphs
Random Structures & Algorithms, 2020 We prove that a random graph G(n,p) , with p above the Hamiltonicity threshold, is typically such that for any r‐coloring of its edges there exists a Hamilton cycle with at least (2/(r+1)−o(1))n edges of the same color.
Lior Gishboliner +2 more
semanticscholar +3 more sources
Tight Hamilton cycles in cherry-quasirandom 3-uniform hypergraphs [PDF]
Combinatorics, probability & computing, 2017 We employ the absorbing-path method in order to prove two results regarding the emergence of tight Hamilton cycles in the so-called two-path or cherry-quasirandom 3-graphs.Our first result asserts that for any fixed real α > 0, cherry-quasirandom 3 ...
Elad Aigner-Horev, Giles Levy
semanticscholar +3 more sources
Hamilton cycles in pseudorandom graphs [PDF]
European Conference on Combinatorics, Graph Theory and Applications, 2023 Finding general conditions which ensure that a graph is Hamiltonian is a central topic in graph theory. An old and well known conjecture in the area states that any $d$-regular $n$-vertex graph $G$ whose second largest eigenvalue in absolute value ...
Stefan Glock +2 more
semanticscholar +1 more source
Universality for transversal Hamilton cycles [PDF]
Bulletin of the London Mathematical Society, 2023 Let G={G1,…,Gm}$\mathbf {G}=\lbrace G_1, \ldots, G_m\rbrace$ be a graph collection on a common vertex set V$V$ of size n$n$ such that δ(Gi)⩾(1+o(1))n/2$\delta (G_i) \geqslant (1+o(1))n/2$ for every i∈[m]$i \in [m]$ .
Candida Bowtell +3 more
semanticscholar +1 more source
Oriented discrepancy of Hamilton cycles [PDF]
Journal of Graph Theory, 2022 We propose the following extension of Dirac's theorem: if G $G$ is a graph with n≥3 $n\ge 3$ vertices and minimum degree δ(G)≥n∕2 $\delta (G)\ge n\unicode{x02215}2$ , then in every orientation of G $G$ there is a Hamilton cycle with at least δ(G) $\delta
Lior Gishboliner +2 more
semanticscholar +1 more source
Hamilton cycles in primitive graphs of order 2rs [PDF]
Ars Math. Contemp., 2022 After long term efforts, it was recently proved in \cite{DKM2} that except for the Peterson graph, every connected vertex-transitive graph of order $rs$ has a Hamilton cycle, where $r$ and $s$ are primes.
Shao-Fei Du, Yao Tian, Hao Yu
semanticscholar +1 more source
Transference for loose Hamilton cycles in random 3‐uniform hypergraphs [PDF]
Random Struct. Algorithms, 2022 A loose Hamilton cycle in a hypergraph is a cyclic sequence of edges covering all vertices in which only every two consecutive edges intersect and do so in exactly one vertex.
Kalina Petrova, Milos Trujic
semanticscholar +1 more source
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
Matchings and Hamilton cycles in hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on
Daniela Kühn, Deryk Osthus
doaj +1 more source
Deformation and damage capacity of thin–walled rods and tubular conduits under alternating loading [PDF]
E3S Web of Conferences, 2023 The paper presents deformation and elastoplastic calculation of thin–walled rods (pipelines) under spatial – alternating loading taking into account damageability of material.
Abdusattarov Abdusamat +2 more
doaj +1 more source