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2. Edge-colouring of graphs and hereditary graph properties

Creator:
Dorfling, Samantha and Vetrík, Tomáš
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
mathematics, grafy, edge-colouring, proper colouring, hereditary graph property, 13, and 51
Language:
English
Description:
Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph G, a hereditary graph property P and l\geqslant 1 we define X{'_{P,l}} to be the minimum number of colours needed to properly colour the edges of G, such that any subgraph of G induced by edges coloured by (at most) l colours is in P. We present a necessary and sufficient condition for the existence of X{'_{P,l}} . We focus on edge-colourings of graphs with respect to the hereditary properties Ok and Sk, where Ok contains all graphs whose components have order at most k+1, and Sk contains all graphs of maximum degree at most k. We determine the value of X{'_{{S_k},l}}(G) for any graph G,k \geqslant 1, l\geqslant 1 and we present a number of results on X{'_{{O_k},l}}(G) ., Samantha Dorfling, Tomáš Vetrík., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On the intersection graph of a finite group

Creator:
Shahsavari, Hossein and Khosravi, Behrooz
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, grafy, mathematics, intersection graph, regular graph, simple group, automorphism group, 13, and 51
Language:
English
Description:
For a finite group $G$, the intersection graph of $G$ which is denoted by $\Gamma(G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq1$. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of ${\rm Aut}(\Gamma(G))$., Hossein Shahsavari, Behrooz Khosravi., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public