Results 61 to 70 of about 1,031 (124)
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
Chorded Pancyclicity in k-Partite Graphs [PDF]
Graphs and Combinatorics, 2018 We prove that for any integers $p\geq k\geq 3$ and any $k$-tuple of positive integers $(n_1,\ldots ,n_k)$ such that $p=\sum _{i=1}^k{n_i}$ and $n_1\geq n_2\geq \ldots \geq n_k$, the condition $n_1\leq {p\over 2}$ is necessary and sufficient for every subgraph of the complete $k$-partite graph $K(n_1,\ldots ,n_k)$ with at least \[{{4 -2p+2n_1+\sum _{i=1}
Daniela Ferrero, Linda Lesniak
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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
Decomposition of the Product of Cycles Based on Degree Partition
Discussiones Mathematicae Graph Theory, 2019 The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n1+ n2+ ・ ・ ・ + nkwith k ≥ 2 and ni≥ 2 for each i. We prove that if k = 2, then G can be decomposed into
Borse Y. M., Shaikh S. R.
doaj +1 more source
Cycles in the burnt pancake graphs
, 2019 The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on $n$ elements generated by prefix reversals. $P_n$ has been shown to have properties that makes it a useful network scheme for parallel processors.
Blanco, Saúl A. +2 more
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Cycles and matchings in randomly perturbed digraphs and hypergraphs
, 2016 We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation.
Krivelevich, Michael +2 more
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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
A Note on Long non-Hamiltonian Cycles in One Class of Digraphs
, 2012 Let $D$ be a strong digraph on $n\geq 4$ vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) $d(x)+d(y)\geq 2n-1$ and $min \{d^+(x)+ d^-(y),d^-(x)+ d^+(y)\}\geq n-1$ for every
Darbinyan, S. Kh., Karapetyan, I. A.
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Journal of Combinatorial Theory, Series B, 1971 AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V(G) |.Theorem. Let G be Hamiltonian and suppose that |E(G)| ≥ n24, where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph Kn2,n2.As a corollary to this theorem it is shown that the Ore conditions for a ...
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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
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