Strong immersions and maximum degree

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10283291" target="_blank" >RIV/00216208:11320/14:10283291 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/130915467" target="_blank" >http://dx.doi.org/10.1137/130915467</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/130915467" target="_blank" >10.1137/130915467</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Strong immersions and maximum degree

Popis výsledku v původním jazyce

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 suchthat 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 unbou

Název v anglickém jazyce

Strong immersions and maximum degree

Popis výsledku anglicky

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 suchthat 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 unbou

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

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Svazek periodika

28

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

177-187

Kód UT WoS článku

000333685700016

EID výsledku v databázi Scopus

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