Turning Cliques into Paths to Achieve Planarity
release_qgpm7w5lvvdgldue3opaplqxca
by
Patrizio Angelini, Peter Eades, Seok-Hee Hong, Karsten Klein, Stephen
Kobourov, Giuseppe Liotta, Alfredo Navarra, Alessandra Tappini
2018
Abstract
Motivated by hybrid graph representations, we introduce and study the
following beyond-planarity problem, which we call h-Clique2Path Planarity:
Given a graph G, whose vertices are partitioned into subsets of size at most
h, each inducing a clique, remove edges from each clique so that the subgraph
induced by each subset is a path, in such a way that the resulting subgraph of
G is planar. We study this problem when G is a simple topological graph,
and establish its complexity in relation to k-planarity. We prove that
h-Clique2Path Planarity is NP-complete even when h=4 and G is a simple
3-plane graph, while it can be solved in linear time, for any h, when G
is 1-plane.
In text/plain
format
Archived Files and Locations
application/pdf 448.2 kB
file_sgsqpi32brgrbfjz27w4nb4nmy
|
arxiv.org (repository) web.archive.org (webarchive) |
1808.08925v1
access all versions, variants, and formats of this works (eg, pre-prints)