Results 41 to 50 of about 635 (107)
The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs
Random Structures &Algorithms, Volume 66, Issue 2, March 2025.ABSTRACT Let μ(G)$$ \mu (G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a Hamiltonian graph, and let μ^(G)$$ \hat{\mu}(G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a pancyclic graph. We study the distributions of μ(G),μ^(G)$$ \mu (G),\hat{\mu}(G) $$ in the context of binomial random ...
Yahav Alon, Michael Anastos
wiley +1 more source
Long cycles in certain graphs of large degree
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 691-697, 2000., 2000 Let G be a connected graph of order n and X = {x ∈ V : d(x) ≥ n/2}. Suppose |X| ≥ 3 and G satisfies the modified Fan′s condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The complexity of this algorithm is O(n2). In case G is 2‐
Pak-Ken Wong
wiley +1 more source
On the Clean Graph of Commutative Artinian Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For a commutative Artinian ring R with unity, the clean graph Cl(R) is a graph with vertices in the form of an ordered pair (e, u), where e is an idempotent and u is a unit of ring R, respectively. Two distinct vertices (e, u) and (f, v) are adjacent in Cl(R) if and only if ef = fe = 0 or uv = vu = 1.
R. Singh +3 more
wiley +1 more source
Graphs which have pancyclic complements
International Journal of Mathematics and Mathematical Sciences, Volume 1, Issue 2, Page 177-185, 1978., 1978 Let p and q denote the number of vertices and edges of a graph G, respectively. Let Δ(G) denote the maximum degree of G, and G¯ the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3 ≤ n ≤ p. For a nonnegative integer k, a connected graph G is said to be of rank k if q = p − 1 + k.
H. Joseph Straight
wiley +1 more source
Discrete Applied Mathematics, 2007 A graph \(G\) is said to be geodesic-pancyclic if every path of length \(d\) between any two vertices \(u\) and \(v\) at distance \(d\) (i.e., the shortest path between \(u\) and \(v\)) can be completed to a cycle of length \(\ell\) for every \(\ell=\max\{2d,3\},\dots,n\).
Hung-Chang Chan +3 more
openaire +2 more sources
Graphs with at most two moplexes
Journal of Graph Theory, Volume 107, Issue 1, Page 38-69, September 2024.Abstract A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free ...
Clément Dallard +4 more
wiley +1 more source
A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs
, 2017 Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$.
Darbinyan, Samvel Kh. +1 more
core +1 more source
Cycles in Random Bipartite Graphs [PDF]
, 2013 In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length $t$
Shang, Yilun
core
The Cycle Spectrum of Claw-free Hamiltonian Graphs [PDF]
, 2013 If $G$ is a claw-free hamiltonian graph of order $n$ and maximum degree $\Delta$ with $\Delta\geq 24$, then $G$ has cycles of at least $\min\left\{ n,\left\lceil\frac{3}{2}\Delta\right\rceil\right\}-2$ many different lengths.Comment: 9 ...
Eckert, Jonas +2 more
core
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