About: Strong immersions and maximum degree

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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/10.1137/130915467
Description	A graph H is strongly immersed in G if G is obtained from H by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct vertices of G (branch vertices), and edges of H are mapped to pairwise edge-disjoint paths in G, each of them joining the branch vertices corresponding to the ends of the edge and not containing any other branch vertices. We show that there exists a function d: N -> N such that for all graphs H and G, if G contains a strong immersion of the star K-1,K-d(Delta(H))vertical bar V(H)vertical bar whose branch vertices are Delta(H)-edge-connected to one another, then H is strongly immersed in G. This has a number of structural consequences for graphs avoiding a strong immersion of H. In particular, a class G of simple 4-edge-connected graphs contains all graphs of maximum degree 4 as strong immersions if and only if G has either unbounded maximum degree or unbounded tree-width. A graph H is strongly immersed in G if G is obtained from H by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct vertices of G (branch vertices), and edges of H are mapped to pairwise edge-disjoint paths in G, each of them joining the branch vertices corresponding to the ends of the edge and not containing any other branch vertices. We show that there exists a function d: N -> N such that for all graphs H and G, if G contains a strong immersion of the star K-1,K-d(Delta(H))vertical bar V(H)vertical bar whose branch vertices are Delta(H)-edge-connected to one another, then H is strongly immersed in G. This has a number of structural consequences for graphs avoiding a strong immersion of H. In particular, a class G of simple 4-edge-connected graphs contains all graphs of maximum degree 4 as strong immersions if and only if G has either unbounded maximum degree or unbounded tree-width. (en)
Title	Strong immersions and maximum degree Strong immersions and maximum degree (en)
skos:prefLabel	Strong immersions and maximum degree Strong immersions and maximum degree (en)
skos:notation	RIV/00216208:11320/14:10283291!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GBP202/12/G061), P(LH12095)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Klimošová, Tereza 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	47788
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10283291
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	structure; maximum degree; graph immersion (en)
http://linked.open.../riv/klicoveSlovo	maximum degree structure graph immersion
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[2F97189338B1]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Discrete Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	New combinatorial algorithms - decompositions, parameterization, efficient solutions Center of excellence - Institute for theoretical computer science (CE-ITI)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	28
http://linked.open...iv/tvurceVysledku	Dvořák, Zdeněk Klimošová, Tereza
http://linked.open...ain/vavai/riv/wos	000333685700016
issn	0895-4801
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/130915467
http://localhost/t...ganizacniJednotka	11320

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