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rdf:type
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rdfs:seeAlso
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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)
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Title
| - Forbidden graphs for tree-depth
- Forbidden graphs for tree-depth (en)
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skos:prefLabel
| - Forbidden graphs for tree-depth
- Forbidden graphs for tree-depth (en)
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skos:notation
| - RIV/00216208:11320/12:10125700!RIV13-MSM-11320___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/12:10125700
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - width; minors; grad; bounded expansion (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - European Journal of Combinatorics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Dvořák, Zdeněk
- Giannopoulou, Archontia C.
- Thilikos, Dimitrios M.
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http://linked.open...ain/vavai/riv/wos
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issn
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number of pages
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http://bibframe.org/vocab/doi
| - 10.1016/j.ejc.2011.09.014
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http://localhost/t...ganizacniJednotka
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