scholarly journals Packing and counting arbitrary Hamilton cycles in random digraphs

2018 ◽  
Vol 54 (3) ◽  
pp. 499-514
Author(s):  
Asaf Ferber ◽  
Eoin Long
Keyword(s):  
Hamilton Cycles ◽  
Random Digraphs

Counting the Number of Hamilton Cycles in Random Digraphs

1992 ◽  
Vol 3 (3) ◽  
pp. 235-241 ◽  
Author(s):  
Alan Frieze ◽  
Stephen Suen
Keyword(s):  
Hamilton Cycles ◽  
Random Digraphs

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.

scholarly journals Random walk on sparse random digraphs

2017 ◽  
Vol 170 (3-4) ◽  
pp. 933-960 ◽  
Author(s):  
Charles Bordenave ◽  
Pietro Caputo ◽  
Justin Salez
Keyword(s):  
Random Walk ◽  
Random Digraphs

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

Hamilton Cycles in Random Regular Digraphs

1997 ◽  
pp. 153-164
Author(s):  
C. Cooper ◽  
A. Frieze ◽  
M. Molloy
Keyword(s):  
Hamilton Cycles
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