5 research outputs found
The stresses on centrally symmetric complexes and the lower bound theorems
In 1987, Stanley conjectured that if a centrally symmetric Cohen--Macaulay
simplicial complex of dimension satisfies
for some , then
for all . Much more recently, Klee, Nevo, Novik, and Zheng conjectured
that if a centrally symmetric simplicial polytope of dimension
satisfies for some , then for all . This note uses stress spaces to prove both of these conjectures.Comment: Simplified statements and proofs of Lemmas 3.3 and 3.4, plus some
minor edits. To appear in Algebraic Combinatoric
Anchored Hyperspaces and Multigraphs
Consider a multigraph as a metric space and p \in X. The anchored hyperspace at is the set
{A \subseteq X : p \in A, A connected and compact}.
In this paper we will prove that is a polytope if in this set is considered the Hausdorff's metric . Further we will show that, if is a locally connected compact metric space such that is a polytope for each p \in X, then must be a multigraph
Advances in Discrete Applied Mathematics and Graph Theory
The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs