# Graphs, groups, and more: celebrating Brian Alspach’s 80th and Dragan Marušič’s 65th birthdays

from 28 May 2018 to 1 June 2018
Koper
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# On decomposing $3$-uniform hypergraphs into loose $m$-cycles

## Speakers

• Prof. Saad EL-ZANATI

## Content

A loose $m$-cycle is a 3-uniform hypergraph with vertex set ${v_1, v_2, \ldots, v_{2m}}$ edge set ${{v_1,v_2,v_3}, {v_3,v_4,v_5}, \ldots, {v_{2m-1},v_{2m},v_1}}$. We consider the problem of decomposing $K_{v}^{(3)}$, the complete 3-uniform hypergraph of order $v$, into edge-disjoint loose $m$-cycles. We settle the problem in the case $m=4$.