The $r$-Matching Sequencibility of Complete Graphs

Abstract

Alspach [Bull. Inst. Combin. Appl. 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(λK n1,...,n k ) where λK n1,...,n k denotes the multi-k-partite k-graph with edge multiplicity λ and parts of sizes n 1 , . . . , n k , respectively. It turns out that these invariants may be given surprisingly precise and somewhat elegant descriptions, in a much more general setting.

The cyclic matching sequenceability of regular graphs

“…edge of X j that is adjacent to an edge in Y j+1 (if x ⌊ 2y 3 ⌋ then we choose X ′ j = X j ). Further, because the last edges of ℓ Y j+1 are those in Y ′ j+1 and y y 1 + 2y 2 by (7), we can apply Lemma 2.6 to obtain an ordering ℓ X ′ j of X ′ j such that ms(ℓ…”