Current browse context:
math.CO
Change to browse by:
References & Citations
Mathematics > Combinatorics
Title: Construction numbers: How to build a graph?
(Submitted on 25 Feb 2023 (v1), last revised 2 Oct 2023 (this version, v3))
Abstract: Counting the number of linear extensions of a partial order was considered by Stanley about 50 years ago. For the partial order on the vertices and edges of a graph determined by inclusion, we call such linear extensions {\it construction sequences} for the graph as each edge follows both of its endpoints. The number of such sequences for paths, cycles, stars, double-stars, and complete graphs is found. For paths, we agree with Stanley (the Tangent numbers) and get formulas for the other classes. Structure and applications are also studied.
Submission history
From: Paul Kainen [view email][v1] Sat, 25 Feb 2023 22:54:27 GMT (15kb)
[v2] Mon, 29 May 2023 18:36:39 GMT (22kb)
[v3] Mon, 2 Oct 2023 17:51:58 GMT (20kb)
Link back to: arXiv, form interface, contact.