Strong immersions and maximum degree

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Strong immersions and maximum degree
Original language 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 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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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