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Statements

Subject Item
n2:RIV%2F49777513%3A23520%2F13%3A43918088%21RIV14-MSM-23520___
rdf:type
skos:Concept n5:Vysledek
rdfs:seeAlso
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p37/pdf
dcterms:description
A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen subdivisions in a permutation graph with no 4-cycles, and give a construction showing that this lower bound is tight up to a constant factor. A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen subdivisions in a permutation graph with no 4-cycles, and give a construction showing that this lower bound is tight up to a constant factor.
dcterms:title
Multiple Petersen subdivisions in permutation graphs Multiple Petersen subdivisions in permutation graphs
skos:prefLabel
Multiple Petersen subdivisions in permutation graphs Multiple Petersen subdivisions in permutation graphs
skos:notation
RIV/49777513:23520/13:43918088!RIV14-MSM-23520___
n5:predkladatel
n6:orjk%3A23520
n7:aktivita
n15:P n15:I
n7:aktivity
I, P(GBP202/12/G061)
n7:cisloPeriodika
1
n7:dodaniDat
n9:2014
n7:domaciTvurceVysledku
n12:1244043
n7:druhVysledku
n18:J
n7:duvernostUdaju
n11:S
n7:entitaPredkladatele
n14:predkladatel
n7:idSjednocenehoVysledku
90146
n7:idVysledku
RIV/49777513:23520/13:43918088
n7:jazykVysledku
n17:eng
n7:klicovaSlova
cograph; Petersen subdivision; permutation graph; graph theory
n7:klicoveSlovo
n10:cograph n10:Petersen%20subdivision n10:permutation%20graph n10:graph%20theory
n7:kodStatuVydavatele
US - Spojené státy americké
n7:kontrolniKodProRIV
[63657F1331B8]
n7:nazevZdroje
ELECTRONIC JOURNAL OF COMBINATORICS
n7:obor
n20:BA
n7:pocetDomacichTvurcuVysledku
1
n7:pocetTvurcuVysledku
3
n7:projekt
n19:GBP202%2F12%2FG061
n7:rokUplatneniVysledku
n9:2013
n7:svazekPeriodika
20
n7:tvurceVysledku
Kaiser, Tomáš Sereni, Jean-Sébastien Yilma, Zelealem B.
s:issn
1077-8926
s:numberOfPages
9
n16:organizacniJednotka
23520