# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Idomatic partitions in direct product graphs

Presented by Mr. Gasper MEKIS
Type: Oral presentation
Track: Domination, Independence and Coloring of Product Graphs

## Content

Partition of $V(G)$ into sets which are independent and dominating is called an {\em idomatic partition}. In this talk results concerning idomatic partitions of direct product of complete graphs will be presented. More precisely, such partitions are characterized up to the product of three complete graphs. For product of four (and more) complete graphs the study is done on idomatic partitions to sets of specific form, called the $T_1$-sets. Idomatic partitions of $\times_{i=1}^t K_{n_i}$ into $T_1$-sets are characterized for $t=4$ and the idea how to construct such a partition in the case of $t-1=p^k$, $p$ is prime, will be presented.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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