### On the structure of 5- and 6-chromatic abstract graphs.

G.A. Dirac (1964)

Journal für die reine und angewandte Mathematik

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G.A. Dirac (1964)

Journal für die reine und angewandte Mathematik

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Jürgen Eufinger (1971)

Journal für die reine und angewandte Mathematik

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Halina Bielak (1999)

Discussiones Mathematicae Graph Theory

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We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.

Don R. Lick (1972)

Journal für die reine und angewandte Mathematik

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G.A. Dirac, B. Toft, B. A. Sorensen (1974)

Journal für die reine und angewandte Mathematik

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O.V. Borodin (1980)

Journal für die reine und angewandte Mathematik

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J.M.S. Simoes-Pereira (1978)

Journal für die reine und angewandte Mathematik

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Robert Janczewski, Michał Małafiejski, Anna Małafiejska (2018)

Discussiones Mathematicae Graph Theory

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G.A. Dirac (1967)

Journal für die reine und angewandte Mathematik

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A. Hajnal (1985)

Publications du Département de mathématiques (Lyon)

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A. Neumaier (1985)

Journal für die reine und angewandte Mathematik

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G.A. Dirac (1974)

Journal für die reine und angewandte Mathematik

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John Mitchem (1978)

Journal für die reine und angewandte Mathematik

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Silvano Delladio (1997)

Journal für die reine und angewandte Mathematik

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John Mitchem, Patrick Morriss, Edward Schmeichel (1997)

Discussiones Mathematicae Graph Theory

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We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and...

Mieczysław Borowiecki, Peter Mihók, Zsolt Tuza, M. Voigt (1999)

Discussiones Mathematicae Graph Theory

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We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".

Halina Bielak (1998)

Discussiones Mathematicae Graph Theory

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In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.

Iztok Peterin (2006)

Discussiones Mathematicae Graph Theory

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Median graphs have many interesting properties. One of them is-in connection with triangle free graphs-the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the convex expansion procedure that characterizes planar median graphs.