Graph colourings and partitions

Yegnanarayanan, V.

doi:10.1016/s0304-3975(00)00231-0

Cited by 14 publications

(8 citation statements)

References 26 publications

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“…The chromatic and achromatic numbers of G are the smallest and the largest number of colors in a complete proper coloring of G, respectively. The concept of achromatic number have been intensely studied in graphs since it was introduced by Harary, Hedetniemi and Prins [14] in 1967, for more references of results related to this parameter see for instance [2,3,1,5,8,15,26]. The achromatic number has been extended to digraphs with two different colorings one by Edwards [11] and another by Sopena [24].…”

Section: Introductionmentioning

confidence: 99%

The Diachromatic Number of Digraphs

Araujo‐Pardo

Montellano-Ballesteros

Olsen

et al. 2018

Electron. J. Combin.

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We consider the extension to directed graphs of the concept of achromatic number in terms of acyclic vertex colorings. The achromatic number have been intensely studied since it was introduced by Harary, Hedetniemi and Prins in 1967. The dichromatic number is a generalization of the chromatic number for digraphs defined by Neumann-Lara in 1982. A coloring of a digraph is an acyclic coloring if each subdigraph induced by each chromatic class is acyclic, and a coloring is complete if for any pair of chromatic classes x, y, there is an arc from x to y and an arc from y to x. The dichromatic and diachromatic numbers are, respectively, the smallest and the largest number of colors in a complete acyclic coloring. We give some general results for the diachromatic number and study it for tournaments. We also show that the interpolation property for complete acyclic colorings does hold and establish Nordhaus-Gaddum relations.

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Section: Introductionmentioning

confidence: 99%

The Diachromatic Number of Digraphs

Araujo‐Pardo

Montellano-Ballesteros

Olsen

et al. 2018

Electron. J. Combin.

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“…Note that, with this definition a perfect graph is denoted by ωχ-perfect. The concept of the ab-perfect graphs was introduced by Christen and Selkow in [8] and extended in [3,2,6,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

The Hadwiger number, chordal graphs and ab-perfection

Rubio-Montiel

2017

AKCE International Journal of Graphs and Combinatorics

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A graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms of the Hadwiger number and we also characterize the families of graphs such that for each induced subgraph H, (1) the Hadwiger number of H is equal to the maximum clique order of H, (2) the Hadwiger number of H is equal to the achromatic number of H, (3) the b-chromatic number is equal to the pseudoachromatic number, (4) the pseudo-b-chromatic number is equal to the pseudoachromatic number, (5) the Hadwiger number of H is equal to the Grundy number of H, and (6) the b-chromatic number is equal to the pseudo-Grundy number.

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“…This definition extends the usual notion of perfect graph introduced by Berge [3], with this notation a perfect graph is denoted by ωχ-perfect. The concept of the ab-perfect graphs was introduced earlier by Christen and Selkow in [7] and extended in [17] and [1,2]. A graph G without an induced subgraph H is called H-free.…”

Section: Introductionmentioning

confidence: 99%