Displaying similar documents to “On the computational complexity of centers locating in a graph”

Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

Edith Hemaspaandra, Jörg Rothe, Holger Spakowski (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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For both the edge deletion heuristic and the maximum-degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r , where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP . To achieve these main results, we also show that the restriction of the vertex cover problem to those graphs...

Radius-invariant graphs

Vojtech Bálint, Ondrej Vacek (2004)

Mathematica Bohemica

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The eccentricity e ( v ) of a vertex v is defined as the distance to a farthest vertex from v . The radius of a graph G is defined as a r ( G ) = min u ∈ V ( G ) { e ( u ) } . A graph G is radius-edge-invariant if r ( G - e ) = r ( G ) for every e ∈ E ( G ) , radius-vertex-invariant if r ( G - v ) = r ( G ) for every v ∈ V ( G ) and radius-adding-invariant if r ( G + e ) = r ( G ) for every e ∈ E ( G ¯ ) . Such classes of graphs are studied in this paper.