On the connectivity of manifold graphs
2015 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 10, 4123-4132 p.Article in journal (Refereed) Published
This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following way: The graph of a d-dimensional simplicial compact manifold M is (2d - b_M)-connected. The parameter b_M has the property that b_M = 0 if the complex M is flag. Hence, our result interpolates between Barnette's theorem (1982) that all d-manifold graphs are (d+1)-connected and Athanasiadis' theorem (2011) that flag d-manifold graphs are 2d-connected. The definition of b_M involves the concept of banner triangulations of manifolds, a generalization of flag triangulations.
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2015. Vol. 143, no 10, 4123-4132 p.
IdentifiersURN: urn:nbn:se:kth:diva-140322DOI: 10.1090/proc/12415ScopusID: 2-s2.0-84938252347OAI: oai:DiVA.org:kth-140322DiVA: diva2:689558
FunderKnut and Alice Wallenberg Foundation
QC 201606022014-01-212014-01-212016-06-02Bibliographically approved