Displaying similar documents to “On doubly light vertices in plane graphs”

On the strong parity chromatic number

Július Czap, Stanislav Jendroľ, František Kardoš (2011)

Discussiones Mathematicae Graph Theory

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A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.

Partitions of some planar graphs into two linear forests

Piotr Borowiecki, Mariusz Hałuszczak (1997)

Discussiones Mathematicae Graph Theory

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A linear forest is a forest in which every component is a path. It is known that the set of vertices V(G) of any outerplanar graph G can be partitioned into two disjoint subsets V₁,V₂ such that induced subgraphs ⟨V₁⟩ and ⟨V₂⟩ are linear forests (we say G has an (LF, LF)-partition). In this paper, we present an extension of the above result to the class of planar graphs with a given number of internal vertices (i.e., vertices that do not belong to the external face at a certain fixed...

Gallai and anti-Gallai graphs of a graph

S. Aparna Lakshmanan, S. B. Rao, A. Vijayakumar (2007)

Mathematica Bohemica

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The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H -free for any finite graph H . The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.