Rainbow Hamilton Cycles in Randomly Colored Randomly Perturbed Dense Graphs

2021 ◽  
Vol 35 (3) ◽  
pp. 1569-1577
Author(s):  
Elad Aigner-Horev ◽  
Dan Hefetz
Keyword(s):  
Hamilton Cycles ◽  
Dense Graphs

scholarly journals A Note on Color-Bias Hamilton Cycles in Dense Graphs

2021 ◽  
Vol 35 (2) ◽  
pp. 970-975
Author(s):  
Andrea Freschi ◽  
Joseph Hyde ◽  
Joanna Lada ◽  
Andrew Treglown
Keyword(s):  
Hamilton Cycles ◽  
Dense Graphs ◽  
Color Bias

scholarly journals Counting and packing Hamilton cycles in dense graphs and oriented graphs

2017 ◽  
Vol 122 ◽  
pp. 196-220 ◽  
Author(s):  
Asaf Ferber ◽  
Michael Krivelevich ◽  
Benny Sudakov
Keyword(s):  
Hamilton Cycles ◽  
Oriented Graphs ◽  
Dense Graphs

Cycle factors in dense graphs

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 309-323 ◽  
Author(s):  
E Fischer
Keyword(s):  
Dense Graphs

scholarly journals Counting Hamilton cycles in Dirac hypergraphs

2020 ◽  
pp. 1-23
Author(s):  
Stefan Glock ◽  
Stephen Gould ◽  
Felix Joos ◽  
Daniela Kühn ◽  
Deryk Osthus
Keyword(s):  
Hamilton Cycle ◽  
Uniform Hypergraph ◽  
Similar Estimate ◽  
Hamilton Cycles

Abstract A tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge. Rödl, Ruciński and Szemerédi proved that for $k\ge 3$ , every k-graph on n vertices with minimum codegree at least $n/2+o(n)$ contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such k-graphs is ${\exp(n\ln n-\Theta(n))}$ . As a corollary, we obtain a similar estimate on the number of Hamilton ${\ell}$ -cycles in such k-graphs for all ${\ell\in\{0,\ldots,k-1\}}$ , which makes progress on a question of Ferber, Krivelevich and Sudakov.

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

Mixed Ramsey Numbers Revisited

2003 ◽  
Vol 12 (5-6) ◽  
pp. 653-660
Author(s):  
C. C. Rousseau ◽  
S. E. Speed
Keyword(s):  
Asymptotic Behaviour ◽  
Ramsey Number ◽  
Open Problems ◽  
Free Graph ◽  
Ramsey Numbers ◽  
Dense Graphs

Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the sequence . Open problems are mentioned throughout the paper.

scholarly journals Hamilton cycles in tensor product of graphs

1998 ◽  
Vol 186 (1-3) ◽  
pp. 1-13 ◽  
Author(s):  
R. Balakrishnan ◽  
P. Paulraja
Keyword(s):  
Tensor Product ◽  
Hamilton Cycles ◽  
Product Of Graphs
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