Euler tours in hypergraphs
Stefan Glock, Felix Joos, Daniela K\"uhn, and Deryk Osthus

TL;DR
This paper proves that quasirandom hypergraphs with certain degree conditions contain tight Euler tours, confirming a longstanding conjecture about universal cycles for subsets.
Contribution
It establishes the existence of tight Euler tours in quasirandom hypergraphs under degree divisibility conditions, confirming a conjecture for complete hypergraphs.
Findings
Quasirandom hypergraphs have tight Euler tours when degrees are divisible by k.
Confirmed the 1989 conjecture on universal cycles for k-subsets.
Provided conditions under which Euler tours exist in hypergraphs.
Abstract
We show that a quasirandom -uniform hypergraph has a tight Euler tour subject to the necessary condition that divides all vertex degrees. The case when is complete confirms a conjecture of Chung, Diaconis and Graham from 1989 on the existence of universal cycles for the -subsets of an -set.
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Taxonomy
TopicsLimits and Structures in Graph Theory · graph theory and CDMA systems · Advanced Topology and Set Theory
