Contact Representations of Planar Graphs: Extending a Partial Representation is Hard - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Conference Papers Year : 2014

Contact Representations of Planar Graphs: Extending a Partial Representation is Hard

Abstract

Planar graphs are known to have geometric representations of various types, e.g. as contacts of disks, triangles or - in the bipartite case - vertical and horizontal segments. It is known that such representations can be drawn in linear time, we here wonder whether it is as easy to decide whether a partial representation can be completed to a representation of the whole graph. We show that in each of the cases above, this problem becomes NP-hard. These are the first classes of geometric graphs where extending partial representations is provably harder than recognition, as opposed to e.g. interval graphs, circle graphs, permutation graphs or even standard representations of plane graphs. On the positive side we give two polynomial time algorithms for the grid contact case. The first one is for the case when all vertical segments are pre-represented (note: the problem remains NP-complete when a subset of the vertical segments is specified, even if none of the horizontals are). Secondly, we show that the case when the vertical segments have only their -coordinates specified (i.e., they are ordered horizontally) is polynomially equivalent to level planarity, which is known to be solvable in polynomial time.
No file

Dates and versions

lirmm-01264271 , version 1 (29-01-2016)

Identifiers

Cite

Steven Chaplick, Paul Dorbec, Jan Kratochvil, Mickaël Montassier, Juraj Stacho. Contact Representations of Planar Graphs: Extending a Partial Representation is Hard. WG 2014 - 40th International Workshop on Graph-Theoretic Concepts in Computer Science, Jun 2014, Nouan-le-fuzelier, France. pp.139-151, ⟨10.1007/978-3-319-12340-0_12⟩. ⟨lirmm-01264271⟩
190 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More