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SEFE without Mapping via Large Induced Outerplane Graphs in Plane Graphs
Author(s) -
Angelini Patrizio,
Evans William,
Frati Fabrizio,
Gudmundsson Joachim
Publication year - 2016
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21884
Subject(s) - combinatorics , planar graph , mathematics , planar straight line graph , book embedding , vertex (graph theory) , outerplanar graph , embedding , polyhedral graph , discrete mathematics , neighbourhood (mathematics) , graph , 1 planar graph , pathwidth , chordal graph , line graph , computer science , artificial intelligence , mathematical analysis
We show that every n ‐vertex planar graph admits a simultaneous embedding without mapping and with fixed edges with any ( n / 2 ) ‐vertex planar graph. In order to achieve this result, we prove that every n ‐vertex plane graph has an induced outerplane subgraph containing at least n / 2 vertices. Also, we show that every n ‐vertex planar graph and every n ‐vertex planar partial 3‐tree admit a simultaneous embedding without mapping and with fixed edges.