منابع مشابه
Graphs Containing Every 2-Factor
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An instance of a Boolean constraint satisfaction problem can be divided into two parts. One part, that we refer to as the factor graph of the instance, specifies for each clause the set of variables that are associated with the clause. The other part, specifies for each of the given clauses what is the constraint that is evaluated on the respective variables. Depending on the allowed choices of...
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The Heawood graph and K3;3 have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2factor hamiltonian graph then either G is a circuit or k 1⁄4 3: Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and K3;3 and conjecture that th...
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Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is α = 7/3.
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We prove a result on the length of a longest cycle in a graph on n vertices that contains a 2-factor and satisfies d(u)+ d(v)+d(w)~> n + 2 for every triple u, v, w of independent vertices. As a corollary we obtain the following improvement of a conjecture of H/iggkvist (1992): Let G be a 2-connected graph on n vertices where every pair of nonadjacent vertices has degree sum at least n-k and ass...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2011
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-011-1066-6