Displaying similar documents to “A σ₃ type condition for heavy cycles in weighted graphs”

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...

An Implicit Weighted Degree Condition For Heavy Cycles

Junqing Cai, Hao Li, Wantao Ning (2014)

Discussiones Mathematicae Graph Theory

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For a vertex v in a weighted graph G, idw(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then...

Constant 2-Labellings And An Application To (R, A, B)-Covering Codes

Sylvain Gravier, Èlise Vandomme (2017)

Discussiones Mathematicae Graph Theory

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We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex set which preserves the sum of the weights of black vertices under some automorphisms. We study constant 2-labellings on four types of vertex-weighted cycles. Our results on cycles allow us to determine (r, a, b)-codes in Z2 whenever...

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator ψ C ϕ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Digraphs are 2-weight choosable.

Khatirinejad, Mahdad, Naserasr, Reza, Newman, Mike, Seamone, Ben, Stevens, Brett (2011)

The Electronic Journal of Combinatorics [electronic only]

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On constant-weight TSP-tours

Scott Jones, P. Mark Kayll, Bojan Mohar, Walter D. Wallis (2003)

Discussiones Mathematicae Graph Theory

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Is it possible to label the edges of Kₙ with distinct integer weights so that every Hamilton cycle has the same total weight? We give a local condition characterizing the labellings that witness this question's perhaps surprising affirmative answer. More generally, we address the question that arises when "Hamilton cycle" is replaced by "k-factor" for nonnegative integers k. Such edge-labellings are in correspondence with certain vertex-labellings, and the link allows us to determine...

Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space

Elke Wolf (2009)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator ψ C ϕ acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.

Embeddings of doubling weighted Besov spaces

Dorothee D. Haroske, Philipp Skandera (2014)

Banach Center Publications

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We study continuous embeddings of Besov spaces of type B p , q s ( ℝ ⁿ , w ) , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.

On-line Ramsey theory for bounded degree graphs.

Butterfield, Jane, Grauman, Tracy, Kinnersley, William B., Milans, Kevin G., Stocker, Christopher, West, Douglas B. (2011)

The Electronic Journal of Combinatorics [electronic only]

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On ( 4 , 1 ) * -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles

Haihui Zhang (2013)

Commentationes Mathematicae Universitatis Carolinae

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A graph G is called ( k , d ) * -choosable if for every list assignment L satisfying | L ( v ) | = k for all v ∈ V ( G ) , there is an L -coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is ( 4 , 1 ) * -choosable.

A weighted graph polynomial from chromatic invariants of knots

Steven D. Noble, Dominic J. A. Welsh (1999)

Annales de l'institut Fourier

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Motivated by the work of Chmutov, Duzhin and Lando on Vassiliev invariants, we define a polynomial on weighted graphs which contains as specialisations the weighted chromatic invariants but also contains many other classical invariants including the Tutte and matching polynomials. It also gives the symmetric function generalisation of the chromatic polynomial introduced by Stanley. We study its complexity and prove hardness results for very restricted classes of graphs.