Results 71 to 80 of about 1,031 (124)
Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs
, 2014 In 1992, Manoussakis conjectured that a strongly 2-connected digraph $D$ on $n$ vertices is hamiltonian if for every two distinct pairs of independent vertices $x,y$ and $w,z$ we have $d(x)+d(y)+d(w)+d(z)\geq 4n-3$.
Ning, Bo
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Pancyclic graphs and linear forests
Discrete Mathematics, 2009 AbstractGiven integers k,s,t with 0≤s≤t and k≥0, a (k,t,s)-linear forest F is a graph that is the vertex disjoint union of t paths with a total of k edges and with s of the paths being single vertices. If the number of single vertex paths is not critical, the forest F will simply be called a (k,t)-linear forest.
Ronald J. Gould +2 more
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Hamiltonian chordal graphs are not cycle extendible [PDF]
, 2014 In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater.
Lafond, Manuel, Seamone, Ben
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Discrete Applied Mathematics, 2013 We introduce the class of (2)-pancyclic graphs, which are simple undirected finite connected graphs of order n having exactly two cycles of length p for each p satisfying [email protected][email protected]?n, analyze their properties, and give several examples of such graphs, among which are the smallest.
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A Survey of Best Monotone Degree Conditions for Graph Properties [PDF]
, 2014 We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 ...
Bauer, D. +7 more
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On pancyclism of hamiltonian graphs
Electronic Notes in Discrete Mathematics, 2000 Abstract Let n and Δ be two integers with Δ ≤ n − 1. We study the set of cycle lengths occurring in any hamiltonian graph G of order n and maximum degree Δ. We show that for the case n/2+1 ≤ Δ ≤ 2n-2/3 this set contains all the integers belonging to the union [3, 2Δ-n+2] ∪ [n-Δ+ 2,Δ+1], and for 2n−2 3 ≤ Δ ≤ n − 1 it contains every integer ...
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Cyclability and pancyclability in bipartite graphs
Discrete Mathematics, 2001 AbstractLet G be a 2-connected bipartite balanced graph of order 2n and bipartition (X,Y). Let S be a subset of X of cardinality at least 3. We define S to be cyclable in G if there exists a cycle through all the vertices of S. Also, G is said S-pancyclable if for every integer l, 3⩽l⩽|S|, there exists a cycle in G that contains exactly l vertices of S.
Denise Amar +2 more
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Super-pancyclic hypergraphs and bipartite graphs
Journal of Combinatorial Theory, Series B, 2020 We find Dirac-type sufficient conditions for a hypergraph $\mathcal H$ with few edges to be hamiltonian. We also show that these conditions provide that $\mathcal H$ is {\em super-pancyclic}, i.e., for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with vertex set $A$.
Dara Zirlin +3 more
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Extremal Results on ℓ-Connected Graphs or Pancyclic Graphs Based on Wiener-Type Indices
MathematicsA graph of order n is called pancyclic if it contains a cycle of length y for every 3≤y≤n. The connectivity of an incomplete graph G, denoted by κ(G), is min{|W||WisavertexcutofG}. A graph G is said to be ℓ-connected if the connectivity κ(G)≥ℓ.
Jing Zeng, Hechao Liu, Lihua You
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Chorded k-pancyclic and weakly k-pancyclic graphs [PDF]
, 2022 Megan Cream, Ronald J. Gould
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