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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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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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Discomfort through Disconnection: Hamilton College’s Online Portrayal of Students of Color [PDF]
, 2021 Hamilton College has a large and unique social media presence that includes depictions and portrayals of the college’s students of color. The manner in which students of color are portrayed holds inherent problems that, although not unique to Hamilton ...
Ghiorsi, Michael, 23
core
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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Random Structures & Algorithms, 2009 AbstractLet G3‐out denote the random graph on vertex set [n] in which each vertex chooses three neighbors uniformly at random. Note that G3‐out has minimum degree 3 and average degree 6. We prove that the probability that G3‐out is Hamiltonian goes to 1 as n tends to infinity. © 2009 Wiley Periodicals, Inc. Random Struct.
Tom Bohman, Alan M. Frieze
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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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Hamilton cycles in almost distance-hereditary graphs
Open Mathematics, 2016 Let G be a graph on n ≥ 3 vertices. A graph G is almost distance-hereditary if each connected induced subgraph H of G has the property dH(x, y) ≤ dG(x, y) + 1 for any pair of vertices x, y ∈ V(H).
Chen Bing, Ning Bo
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A Note on Barnette’s Conjecture
Discussiones Mathematicae Graph Theory, 2013 Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c > 0 such that each graph G of this class contains a path on at least c ...
Harant Jochen
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Cards of fixed points of some Lotka-Volterra operators [PDF]
E-Journal of Analysis and Applied MathematicsThe paper considers a special type of the Lotka-Volterra operator operating in a four-dimensional simplex. The tournament corresponding to this operator has four cyclic triples. All kinds of fixed point cards are built for it. It is proved which types of
Dilfuza B. Eshmamatova +1 more
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Notes on sufficient conditions for a graph to be Hamiltonian
International Journal of Mathematics and Mathematical Sciences, 1991 The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem.
Michael Joseph Paul +2 more
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