Hypergraph convolution and hypergraph attention

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...

Hypergraph Colouring and Degeneracy

A hypergraph is d-degenerate if every subhypergraph has a vertex of degree at most d. A greedy algorithm colours every such hypergraph with at most d+ 1 colours. We show that this bound is tight, by constructing an r-uniform d-degenerate hypergraph with chromatic number d + 1 for all r ≥ 2 and d ≥ 1. Moreover, the hypergraph is triangle-free, where a triangle in an r-uniform hypergraph consists...

Hypergraph functor and attachment

Since the inception of the notion of fuzzy topology much attention was paid to the possible means of interaction between fuzzy and crisp topological settings, in order to see whether fuzzy topology was doing anything new. In particular, different functors relating the categories Top of topological spaces and L-Top of Ltopological spaces (L being a suitable complete lattice) appeared in the lite...