Displaying similar documents to “Optimal Cycles in Doubly Weighted Graphs and Approximation of Bivariate Functions by Univariate Ones.”

Heavy cycles in weighted graphs

J. Adrian Bondy, Hajo J. Broersma, Jan van den Heuvel, Henk Jan Veldman (2002)

Discussiones Mathematicae Graph Theory

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An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known result by Dirac for unweighted graphs is due to Bondy and Fan. Let G be a 2-connected weighted...

A σ₃ type condition for heavy cycles in weighted graphs

Shenggui Zhang, Xueliang Li, Hajo Broersma (2001)

Discussiones Mathematicae Graph Theory

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A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d w ( v ) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz)...

The Total Acquisition Number Of The Randomly Weighted Path

Anant Godbole, Elizabeth Kelley, Emily Kurtz, Paweł Prałat, Yiguang Zhang (2017)

Discussiones Mathematicae Graph Theory

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There exists a significant body of work on determining the acquisition number at(G) of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected...

Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak, Kamil Powroźnik (2015)

Annales UMCS, Mathematica

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In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs

Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak, Kamil Powroźnik (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.

Cycles in graphs and related problems

Antoni Marczyk

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Our aim is to survey results in graph theory centered around four themes: hamiltonian graphs, pancyclic graphs, cycles through vertices and the cycle structure in a graph. We focus on problems related to the closure result of Bondy and Chvátal, which is a common generalization of two fundamental theorems due to Dirac and Ore. We also describe a number of proof techniques in this domain. Aside from the closure operation we give some applications of Ramsey theory in the research of cycle...