t-Strong cliques and the degree-diameter problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00112696" target="_blank" >RIV/00216224:14330/19:00112696 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1258/762" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1258/762</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
t-Strong cliques and the degree-diameter problem
Original language description
For a graph G, L(G)(t) is the t-th power of the line graph of G that is, vertices of L(G)(t) are edges of G and two edges e, f is an element of E(G) are adjacent in L(G)(t) if G contains a path with at most t vertices that starts in a vertex of e and ends in a vertex of f. The t-strong chromatic index of G is the chromatic number of L(G)(t) and a t-strong clique in G is a clique in L(G)(t). Finding upper bounds for the t-strong chromatic index and t-strong clique are problems related to two famous problems: the conjecture of Erdos and NeAetfil concerning the strong chromatic index and the degree/diameter problem. We prove that the size of a t-strong clique in a graph with maximum degree Delta is at most 1.75 Delta(t) + O (Delta t(-1)), and for bipartite graphs the upper bound is at most Delta(t) + O (Delta t(-1)). We also show results for some special classes of graphs: K-1,K-r-free graphs and graphs with a large girth.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF16_027%2F0008360" target="_blank" >EF16_027/0008360: Postdoc@MUNI</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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