About: Forbidden graphs for tree-depth

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.ejc.2011.09.014
Description	For every k }= 0, we define G(k) as the class of graphs with tree-depth at most k, i.e. the class containing every graph G admitting a valid colouring rho : V(G) -> {1, ... , k} such that every (x, y)-path between two vertices where rho(x) = rho(y) contains a vertex z where rho(z) > rho(x). In this paper, we study the set of graphs not belonging in G(k) that are minimal with respect to the minor/subgraph/induced subgraph relation (obstructions of G(k)). We determine these sets for k {= 3 for each relation and prove a structural lemma for creating obstructions from simpler ones. As a consequence, we obtain a precise characterization of all acyclic obstructions of G(k) and we prove that there are exactly 1/2 2(2k-1-k)(1+2(2k-1-k)). Finally, we prove that each obstruction of G(k) has at most 2(2k-1) vertices. For every k }= 0, we define G(k) as the class of graphs with tree-depth at most k, i.e. the class containing every graph G admitting a valid colouring rho : V(G) -> {1, ... , k} such that every (x, y)-path between two vertices where rho(x) = rho(y) contains a vertex z where rho(z) > rho(x). In this paper, we study the set of graphs not belonging in G(k) that are minimal with respect to the minor/subgraph/induced subgraph relation (obstructions of G(k)). We determine these sets for k {= 3 for each relation and prove a structural lemma for creating obstructions from simpler ones. As a consequence, we obtain a precise characterization of all acyclic obstructions of G(k) and we prove that there are exactly 1/2 2(2k-1-k)(1+2(2k-1-k)). Finally, we prove that each obstruction of G(k) has at most 2(2k-1) vertices. (en)
Title	Forbidden graphs for tree-depth Forbidden graphs for tree-depth (en)
skos:prefLabel	Forbidden graphs for tree-depth Forbidden graphs for tree-depth (en)
skos:notation	RIV/00216208:11320/12:10125700!RIV13-MSM-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1M0545)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Dvořák, Zdeněk
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	136924
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10125700
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	width; minors; grad; bounded expansion (en)
http://linked.open.../riv/klicoveSlovo	minors width bounded expansion grad
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[D2CC806A0A9B]
http://linked.open...i/riv/nazevZdroje	European Journal of Combinatorics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	33
http://linked.open...iv/tvurceVysledku	Dvořák, Zdeněk Giannopoulou, Archontia C. Thilikos, Dimitrios M.
http://linked.open...ain/vavai/riv/wos	000301306200020
issn	0195-6698
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.ejc.2011.09.014
http://localhost/t...ganizacniJednotka	11320

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