Results 291 to 300 of about 3,218,251 (319)

Hamilton Cycles

The Discrete Mathematical Charms of Paul Erdős, 2021
Let us prove that it has no 10-cycle, so the circumference is 9. We think of the Petersen graph as an outside 5-cycle and an inside 5-cycle, connected by 5 links.
Frank de Zeeuw
semanticscholar   +2 more sources

Tight Hamilton cycles with high discrepancy

Combinatorics, probability & computing, 2023
In this paper, we study discrepancy questions for spanning subgraphs of $k$ -uniform hypergraphs. Our main result is that, for any integers $k \ge 3$ and $r \ge 2$
Lior Gishboliner, Stefan Glock, Amedeo Sgueglia   +2 more
semanticscholar   +1 more source

Powers of Hamilton Cycles of High Discrepancy are Unavoidable

Electronic Journal of Combinatorics, 2021
The Pósa-Seymour conjecture asserts that every graph on n vertices with minimum degree at least (1−1/(r +1))n contains the r-th power of a Hamilton cycle. Komlós, Sárközy and Szemerédi famously proved the conjecture for large n.
Domagoj Bradač
semanticscholar   +1 more source

Tight bounds for powers of Hamilton cycles in tournaments

J. Comb. Theory B, 2021
A basic result in graph theory says that any $n$-vertex tournament with in- and out-degrees larger than $\frac{n-2}{4}$ contains a Hamilton cycle, and this is tight.
Nemanja Draganić, David Munhá Correia, B. Sudakov   +2 more
semanticscholar   +1 more source

Rainbow Hamilton Cycles in Randomly Colored Randomly Perturbed Dense Graphs

SIAM Journal on Discrete Mathematics, 2020
Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs of $G$ is referred to as a (random) {\sl perturbation} of $G$.
Elad Aigner-Horev, Dan Hefetz
semanticscholar   +1 more source

Oriented hamilton cycles in digraphs

Journal of Graph Theory, 1995
AbstractWe show that a directed graph of order n will contain n‐cycles of every orientation, provided each vertex has indegree and outdegree at least (1/2 + n‐1/6)n and n is sufficiently large. © 1995 John Wiley & Sons, Inc.
Häggkvist, Roland, Thomason, Andrew
openaire   +1 more source

Packing Directed Hamilton Cycles Online

SIAM Journal on Discrete Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anastos, Michael, Briggs, Joseph
openaire   +2 more sources

Independence trees and Hamilton cycles

Journal of Graph Theory, 1998
Summary: Let \(G\) be a connected graph on \(n\) vertices. A spanning tree \(T\) of \(G\) is called an independence tree, if the set of end vertices of \(T\) (vertices with degree one in \(T\)) is an independent set in \(G\). If \(G\) has an independence tree, then \(\alpha_t(G)\) denotes the maximum number of end vertices of an independence tree of ...
Broersma, Haitze J., Tuinstra, Hilde
openaire   +3 more sources

Stability of Transversal Hamilton Cycles and Paths

Electronic Journal of Combinatorics
Given graphs $G_1,\ldots,G_s$ all on a common vertex set and a graph $H$ with $e(H) = s$, a copy of $H$ is transversal or rainbow if it contains one edge from each $G_i$. We establish a stability result for transversal Hamilton cycles: the minimum degree
Yangyang Cheng, Katherine Staden
semanticscholar   +1 more source