# The $r$-matching sequencibility of complete multi-$k$-partite $k$-graphs

## TL;DR

This paper extends the concept of maximal matching sequencibility from graphs to hypergraphs, specifically analyzing multi-$k$-partite $k$-graphs, and provides precise characterizations of these invariants.

## Contribution

It introduces the hypergraph analogue of matching sequencibility and determines exact values for multi-$k$-partite $k$-graphs, generalizing previous graph results.

## Key findings

- Exact values for $ms( ext{multi-$k$-partite $k$-graphs})$
- Surprisingly elegant descriptions of these invariants
- Generalization of graph matching sequencibility to hypergraphs

## Abstract

Alspach [{\sl Bull. Inst. Combin. Appl.}~{\bf 52} (2008), 7--20] defined the maximal matching sequencibility of a graph $G$, denoted~$ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$ consecutive edges form a matching. In this paper, we consider the natural analogue for hypergraphs of this and related results and determine $ms(\lambda\mathcal{K}_{n_1,\ldots, n_k})$ where $\lambda\mathcal{K}_{n_1,\ldots, n_k}$ denotes the multi-$k$-partite $k$-graph with edge multiplicity $\lambda$ and parts of sizes $n_1,\ldots,n_k$, respectively. It turns out that these invariants may be given surprisingly precise and somewhat elegant descriptions, in a much more general setting.