Packing trees into 1-planar graphs

Felice De Luca, Emilio Di Giacomo, Seok Hee Hong, Stephen Kobourov, William Lenhart, Giuseppe Liotta, Henk Meijer, Alessandra Tappini, Stephen Wismath

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce and study the 1-planar packing problem: Given k graphs with n vertices G1…, Gk, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each Gi is a tree and k = 3. We prove that a triple consisting of three caterpillars or of two caterpillars and a path may not admit a 1-planar packing, while two paths and a special type of caterpillar always have one. We then study 1-planar packings with few crossings and prove that three paths (resp. cycles) admit a 1-planar packing with at most seven (resp. fourteen) crossings. We finally show that a quadruple consisting of three paths and a perfect matching with n ≥ 12 vertices admits a 1-planar packing, while such a packing does not exist if n ≤ 10.

Original languageEnglish (US)
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
EditorsM. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
PublisherSpringer
Pages81-93
Number of pages13
ISBN (Print)9783030398804
DOIs
StatePublished - 2020
Event14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore
Duration: Mar 31 2020Apr 2 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12049 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
CountrySingapore
CitySingapore
Period3/31/204/2/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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