Displaying similar documents to “The list linear arboricity of planar graphs”

Pₘ-saturated bipartite graphs with minimum size

Aneta Dudek, A. Paweł Wojda (2004)

Discussiones Mathematicae Graph Theory

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A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.

α-Labelings of a Class of Generalized Petersen Graphs

Anna Benini, Anita Pasotti (2015)

Discussiones Mathematicae Graph Theory

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An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class...

The edge C₄ graph of some graph classes

Manju K. Menon, A. Vijayakumar (2010)

Discussiones Mathematicae Graph Theory

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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...

Generalized colorings and avoidable orientations

Jenő Szigeti, Zsolt Tuza (1997)

Discussiones Mathematicae Graph Theory

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Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family...

A new proof of the four-colour theorem.

Robertson, Neil, Sanders, Daniel P., Seymour, Paul, Thomas, Robin (1996)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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