Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: total chromatic number

Sortuj według:

Ogranicz wyniki do:

Chromatic Properties of the Pancake Graphs

100%

Konstantinova E.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

777-787

Chromatic properties of the Pancake graphs Pn, n ⩾ 2, that are Cayley graphs on the symmetric group Symn generated by prefix-reversals are investigated in the paper. It is proved that for any n ⩾ 3 the total chromatic number of Pn is n, and it is shown that the chromatic index of Pn is n − 1. We present upper bounds on the chromatic number of the Pancake graphs Pn, which improve Brooks’ bound for n ⩾ 7 and Katlin’s bound for n ⩽ 28. Algorithms of a total n-coloring and a proper (n − 1)-coloring are given.

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Edge colorings and total colorings of integer distance graphs

86%

Kemnitz A., Marangio M.

Discussiones Mathematicae Graph Theory

2002

tom 22

nr 1

149-158

An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Kemnitz A.

1 Konstantinova E.

1 Marangio M.

1 2017

1 2002

Wyniki wyszukiwania

Chromatic Properties of the Pancake Graphs

Edge colorings and total colorings of integer distance graphs