Displaying similar documents to “Distribution of crossings, nestings and alignments of two edges in matchings and partitions.”

A path(ological) partition problem

Izak Broere, Michael Dorfling, Jean E. Dunbar, Marietjie Frick (1998)

Discussiones Mathematicae Graph Theory

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Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positive integers such that τ(G) = k₁ + k₂. The question at hand is whether the vertex set V(G) can be partitioned into two subsets V₁ and V₂ such that τ(G[V₁] ) ≤ k₁ and τ(G[V₂] ) ≤ k₂. We show that several classes of graphs have this partition property.

Finding H -partitions efficiently

Simone Dantas, Celina M. H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the concept of an H -partition of the vertex set of a graph G , which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H , with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties:...