2020 年 E103.A 巻 2 号 p. 510-522
One goal in stack-queue mixed layouts of a graph subdivision is to obtain a layout with minimum number of subdivision vertices per edge when the number of stacks and queues are given. Dujmović and Wood showed that for every integer s, q>0, every graph G has an s-stack q-queue subdivision layout with 4⌈log(s+q)q sn(G)⌉ (resp. 2+4⌈log(s+q)q qn(G)⌉) division vertices per edge, where sn(G) (resp. qn(G)) is the stack number (resp. queue number) of G. This paper improves these results by showing that for every integer s, q>0, every graph G has an s-stack q-queue subdivision layout with at most 2⌈logs+q-1sn(G)⌉ (resp. at most 2⌈logs+q-1qn(G)⌉ +4) division vertices per edge. That is, this paper improves previous results more, for graphs with larger stack number sn(G) or queue number qn(G) than given integers s and q. Also, the larger the given integer s is, the more this paper improves previous results.
