Hypergraph motifs

Hypergraph Rewriting

In their pioneering paper [KB70], Knuth and Bendix showed that con uence (or, equivalently, the Church-Rosser property) is decidable for terminating term rewriting systems. It su ces to compute all critical pairs t s ! u of rewrite steps in which s is the superposition of the left-hand sides of two rules, and to check whether t and u reduce to a common term. This procedure is justi ed by the so...

Hypergraph Codes

Hypergraph Games

The above is called the “strong” version of the game. In the “weak” version, also called “maker-breaker”, the second player’s aim is not to occupy a winning set but just to prevent the first player from doing so. The interest is both for general theorems about games and also in particular games of interest, like the Hales-Jewett game (multi-dimensional noughts & crosses). Roughly speaking, a fa...

Hardness for Hypergraph Coloring

We show that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 2(logN) 1/10−o(1) colors, where N is the number of vertices. There has been much focus on hardness of hypergraph coloring recently. In [17], Guruswami, H̊astad, Harsha, Srinivasan and Varma showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 22Ω( √ log logN) colors. Their result is obtain...

Quantum hypergraph states

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalized stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states whic...