Results 11 to 20 of about 878 (132)

Alternating-Pancyclism in 2-Edge-Colored Graphs

Discussiones Mathematicae Graph Theory, 2021
An alternating cycle in a 2-edge-colored graph is a cycle such that any two consecutive edges have different colors. Let G1, . . ., Gkbe a collection of pairwise vertex disjoint 2-edge-colored graphs. The colored generalized sum of G1, . . ., Gk, denoted
Cordero-Michel Narda, Galeana-Sánchez Hortensia   +1 more
doaj   +2 more sources

Edge pancyclic derangement graphs [PDF]

, 2022
7 pages, 1 ...
Zequn Lv, Mengyu Cao, Mei Lu
openalex   +3 more sources

Rainbow Pancyclicity in Graph Systems [PDF]

The Electronic Journal of Combinatorics, 2021
 Let $G_1,\ldots,G_n$ be graphs on the same vertex set of size $n$, each graph with minimum degree $\delta(G_i)\ge n/2$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e. a cycle with edge set $\{e_1,\ldots,e_n\}$ such that $e_i\in E(G_i)$ for $1\leq i \leq n$.
Yangyang Cheng, Guanghui Wang, Yi Zhao
openalex   +4 more sources

New sufficient conditions for Hamiltonian paths. [PDF]

ScientificWorldJournal, 2014
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Rahman MS, Kaykobad M, Firoz JS.
europepmc   +2 more sources

A SUFFICIENT CONDITION FOR PANCYCLIC GRAPHS [PDF]

Bulletin of the Australian Mathematical Society
Abstract A graph G is called an $[s,t]$ -graph if any induced subgraph of G of
Xingzhi Zhan
  +5 more sources

Sparse pancyclic subgraphs of random graphs [PDF]

SIAM Journal on Discrete Mathematics, 2023
It is known that the complete graph $K_n$ contains a pancyclic subgraph with $n+(1+o(1))\cdot \log _2 n$ edges, and that there is no pancyclic graph on $n$ vertices with fewer than $n+\log _2 (n-1) -1$ edges. We show that, with high probability, $G(n,p)$ contains a pancyclic subgraph with $n+(1+o(1))\log_2 n$ edges for $p \ge p^*$, where $p^*=(1+o(1 ...
Yahav Alon, Michael Krivelevich
openalex   +3 more sources

Weakly pancyclic graphs [PDF]

Journal of Graph Theory, 1998
Summary: In generalizing the concept of a pancyclic graph, we say that a graph is ``weakly pancyclic'' if it contains cycles of every length between the length of a shortest and a longest cycle. In this paper it is shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic are considerably weaker than those required ...
Stephan Brandt, Ralph J. Faudree, Wayne Goddard   +2 more
openalex   +3 more sources

On pancyclic line graphs [PDF]

Czechoslovak Mathematical Journal, 1978
Ladislav Nebeský
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PANCYCLICITY IN LINE GRAPHS [PDF]

Acta Mathematica Scientia, 1998
For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
Daniela Ferrero, Linda Lesniak
openaire   +6 more sources

Chorded k-pancyclic and weakly k-pancyclic graphs [PDF]

Discussiones Mathematicae Graph Theory, 2022
Summary: As natural relaxations of pancyclic graphs, we say a graph \(G\) is \(k\)-pancyclic if \(G\) contains cycles of each length from \(k\) to \(|V(G)|\) and \(G\) is weakly pancyclic if it contains cycles of all lengths from the girth to the circumference of \(G\), while \(G\) is weakly \(k\)-pancyclic if it contains cycles of all lengths from \(k\
Megan Cream, Ronald J. Gould
openalex   +4 more sources