Results 31 to 40 of about 105 (94)

Local properties of graphs that induce global cycle properties [PDF]

Opuscula Mathematica
A graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic.
Yanyan Wang, Xiaojing Yang
doaj   +1 more source

Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments

Proceedings of the London Mathematical Society, Volume 109, Issue 3, Page 733-762, September 2014., 2014
A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)‐connected tournament contains k edge‐disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1)=1. So far, even the existence of f(2) was open.
Daniela Kühn, John Lapinskas, Deryk Osthus, Viresh Patel   +3 more
wiley   +1 more source

Eulerian and pancyclic zero-divisor graphs of ordered sets

AKCE International Journal of Graphs and Combinatorics
In this paper, we determine when the zero-divisor graph of a special class of a finite pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic, and edge pancyclic properties of the complement of a zero-divisor graph of ...
Nilesh Khandekar, Vinayak Joshi
doaj   +1 more source

Locally Pancyclic Graphs

Journal of Combinatorial Theory, Series B, 1999
It was shown by \textit{J. A. Bondy} [Stud. Sci. Math. Hung. 4, 473-475 (1969; Zbl 0184.27702)] that if \(G\) is a graph of order \(n\) in which \(d_G(x) + d_G(y) \geq n\) for each pair of nonadjacent vertices \(x\) and \(y\) of \(G\), then \(G\) is either pancyclic or the complete bipartite graph \(K_{n/2,n/2}\).
openaire   +2 more sources

On pancyclism in hamiltonian graphs

Discrete Mathematics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kouider, Mekkia, Marczyk, Antoni
openaire   +2 more sources

An Efficient Hierarchy Algorithm for Community Detection in Complex Networks

Mathematical Problems in Engineering, Volume 2014, Issue 1, 2014., 2014
Community structure is one of the most fundamental and important topology characteristics of complex networks. The research on community structure has wide applications and is very important for analyzing the topology structure, understanding the functions, finding the hidden properties, and forecasting the time‐varying of the networks.
Lili Zhang, Qing Ye, Yehong Shao, Chenming Li, Hongmin Gao, Ren-Jieh Kuo   +5 more
wiley   +1 more source

Forbidden subgraphs for chorded pancyclicity

Discrete Mathematics, 2017
We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length $4, 5, \ldots, |V(G)|
Megan Cream, Ronald J. Gould, Victor Larsen   +2 more
openaire   +3 more sources

Graph Invariants and Large Cycles: A Survey

International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011
Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations
Zh. G. Nikoghosyan, Howard Bell
wiley   +1 more source

Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords

Discussiones Mathematicae Graph Theory, 2015
It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima, Rutherford Carrie G., Whitty Robin W.   +2 more
doaj   +1 more source

Note on Hamiltonicity of Basis Graphs of Even Delta‐Matroids

Journal of Graph Theory, Volume 109, Issue 4, Page 446-453, August 2025.
ABSTRACT We show that the basis graph of an even delta‐matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges e and f sharing a common end, it has a Hamiltonian cycle using e and avoiding f unless it has at most two vertices or it is a cycle of length at most four.
Donggyu Kim, Sang‐il Oum
wiley   +1 more source