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Vertex-distinguishing edge-colorings of linear forests

100%

Cichacz S., Przybyło J.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

95-103

In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.

Three edge-coloring conjectures

75%

Schelp R.

Discussiones Mathematicae Graph Theory

2002

tom 22

nr 1

173-182

The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Cichacz S.

1 Przybyło J.

1 Schelp R.

1 2010

1 2002

Wyniki wyszukiwania

Vertex-distinguishing edge-colorings of linear forests

Three edge-coloring conjectures