Results 31 to 40 of about 60,523 (284)
Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
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Counting Hamilton cycles in Dirac hypergraphs [PDF]
Combinatorics, Probability and Computing, 2020 AbstractA tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge. Rödl, Ruciński and Szemerédi proved that for $k\ge 3$ , every k-graph on n vertices with minimum codegree at least $n/2+o(n)$ contains a tight Hamilton cycle.
Glock, Stefan +4 more
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Hamilton Cycles in Double Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2019 Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are
Sakamoto Yutaro
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Hamilton-connected properties in cartesian product [PDF]
Transactions on Combinatorics, 2012 In this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. We present some sufficient and necessary conditions for $GBox H$ being hamilton-connected when $G$ is a hamilton-connected ...
Rushengul Hoshur, Elkin Vumar
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Extending Cycles Locally to Hamilton Cycles [PDF]
The Electronic Journal of Combinatorics, 2016 A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle $S^1$ that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs.
Florian Lehner +2 more
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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 +2 more
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Perfect Set of Euler Tours of Kp,p,p
Discussiones Mathematicae Graph Theory, 2016 Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence ...
Govindan T., Muthusamy A.
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Edge condition for hamiltonicity in balanced tripartite graphs [PDF]
Opuscula Mathematica, 2009 A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order \(2n\) obtained from the complete balanced bipartite \(K_{n,n}\) by removing at most \(n-2\) edges, is bipancyclic.
Janusz Adamus
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Electronic Journal of Graph Theory and Applications, 2021 A Hamiltonian graph G = (V,E) is called hyper-Hamiltonian if G-v is Hamiltonian for any v ∈ V(G). G is called a circulant if its automorphism group contains a |V(G)|-cycle.
Zbigniew R. Bogdanowicz
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Rainbow Hamilton Cycles in Uniform Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2012 Let $K_n^{(k)}$ be the complete $k$-uniform hypergraph, $k\ge3$, and let $\ell$ be an integer such that $1\le \ell\le k-1$ and $k-\ell$ divides $n$. An $\ell$-overlapping Hamilton cycle in $K_n^{(k)}$ is a spanning subhypergraph $C$ of $K_n^{(k)}$ with $n/(k-\ell)$ edges and such that for some cyclic ordering of the vertices each edge of $C$ consists
Andrzej Ruciński +2 more
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