Abstract
We study the question of whether a sequence d=(d1,…,dn) of positive integers is the degree sequence of some outerplanar graph G. If so, G is an outerplanar realization of d and d is an outerplanaric sequence. The case where ∑d≤2n−2 is easy, as d has a realization by a forest. In this paper, we consider the family D of all sequences d of even sum 2n≤∑d≤4n−6−2ω1, where ωx is the number of x's in d. We partition D into two disjoint subfamilies, D=DNOP∪D2PBE, such that every sequence in DNOP is provably non-outerplanaric, and every sequence in D2PBE is given a realizing graph G enjoying a 2-page book embedding (and moreover, one of the pages is also bipartite).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
