Abstrakt
A page (queue) with respect to a vertex ordering of a graph is a set of edges such that no two edges cross (nest), i.e., have their endpoints ordered in an abab-pattern (abba-pattern). A union page (union queue) is a vertex-disjoint union of pages (queues).
The union page number (union queue number) of a graph is the smallest k such that there is a vertex ordering and a partition of the edges into k union pages (union queues). The local page number (local queue number) is the smallest k for which there is a vertex ordering and a partition of the edges into pages (queues) such that each vertex has incident edges in at most k pages (queues).
We present upper and lower bounds on these four parameters for the complete graph Kn on n vertices. In three cases we obtain the exact result up to an additive constant.
In particular, the local page number of Kn is n/ 3 +- O(1 ), while its local and union queue number is (1-1/2)n+-O(1). The union page number of Kn is between n/ 3 - O(1 ) and 4 n/ 9 + O(1 ). (C) 2021, Springer Nature Switzerland AG.