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DOI: 10.4230/LIPIcs.MFCS.2017.76
URN: urn:nbn:de:0030-drops-80883
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8088/
Cosme Llópez, Enric ; Pous, Damien
K4-free Graphs as a Free Algebra
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Abstract
Graphs of treewidth at most two are the ones excluding the clique with four vertices as a minor. Equivalently, they are the graphs whose biconnected components are series-parallel. We turn those graphs into a free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting them: in addition to series and parallel compositions, it suffices to consider the neutral elements of those operations and a unary transpose operation. Then we give a finite equational presentation and we prove it complete: two terms from the syntax are congruent if and only if they denote the same graph.
BibTeX - Entry
@InProceedings{cosmellpez_et_al:LIPIcs:2017:8088,
author = {Enric Cosme Ll{\'o}pez and Damien Pous},
title = {{K4-free Graphs as a Free Algebra}},
booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
pages = {76:1--76:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-046-0},
ISSN = {1868-8969},
year = {2017},
volume = {83},
editor = {Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8088},
URN = {urn:nbn:de:0030-drops-80883},
doi = {10.4230/LIPIcs.MFCS.2017.76},
annote = {Keywords: Universal Algebra, Graph theory, Axiomatisation, Tree decompositions, Graph minors}
}
| Keywords: | Universal Algebra, Graph theory, Axiomatisation, Tree decompositions, Graph minors | |
| Seminar: | 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 01.12.2017 |
