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):  
2021 ◽  
Vol 35 (2) ◽  
pp. 970-975
Author(s):  
Andrea Freschi ◽  
Joseph Hyde ◽  
Joanna Lada ◽  
Andrew Treglown

2017 ◽  
Vol 122 ◽  
pp. 196-220 ◽  
Author(s):  
Asaf Ferber ◽  
Michael Krivelevich ◽  
Benny Sudakov

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

Author(s):  
Stefan Glock ◽  
Stephen Gould ◽  
Felix Joos ◽  
Daniela Kühn ◽  
Deryk Osthus

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.


2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen

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.


2003 ◽  
Vol 12 (5-6) ◽  
pp. 653-660
Author(s):  
C. C. Rousseau ◽  
S. E. Speed

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.


1998 ◽  
Vol 186 (1-3) ◽  
pp. 1-13 ◽  
Author(s):  
R. Balakrishnan ◽  
P. Paulraja

Sign in / Sign up

Export Citation Format

Share Document