SEFE without Mapping via Large Induced Outerplane Graphs in Plane Graphs | Zendy

Angelini Patrizio | Zendy; Evans William | Zendy; Frati Fabrizio | Zendy; Gudmundsson Joachim | Zendy

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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.

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