Planar subgraphs without low-degree nodes

Authors:
Evangelos Kranakis;Oscar Morales Ponce;Jukka Suomela
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada;Helsinki Institute for Information Technology, University of Helsinki, Finland
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 2) leads to NP-hard problems.