We prove that the projective dimension of any (hyper) graph can be bounded from above by
the (Castelnuovo-Mumford) regularity of its Levi graph (or incidence bipartite graph). This in …

We study the relationship between the projective dimension of a squarefree monomial ideal
and the domination parameters of the associated graph or clutter. In particular, we show that …

This article emphasizes an extension of the study of metric and par-tition dimension to
hypergraphs. We give a sharp lower bounds for the metric and partition dimension of …

We construct several pairwise-incomparable bounds on the projective dimensions of edge
ideals. Our bounds use combinatorial properties of the associated graphs. In particular, we …

The strong isometric dimension of a reflexive graph is related to its injective hull: both deal
with embedding reflexive graphs in the strong product of paths. We give several upper and …

The Gram dimension $\gd (G) $ of a graph is the smallest integer $ k\ge 1$ such that, for
every assignment of unit vectors to the nodes of the graph, there exists another assignment …

Let $ I (G) $ be the edge ideal of a graph $ G $ with $| V (G)|= n $ and $ R=\mathbb {K}[x\mid
x\in V (G)] $ be a polynomial ring in $ n $ variables over a field $\mathbb {K} $. In this paper …

The orthogonality dimension of a graph $ G=(V, E) $ over a field $\mathbb {F} $ is the
smallest integer $ t $ for which there exists an assignment of a vector $ u_v\in\mathbb {F}^ t …

The convex dimension of a k-uniform hypergraph is the smallest dimension d for which there
is an injective mapping of its vertices into R d such that the set of k-barycenters of all …

arXiv:2405.11174v1 [math.CO] 18 May 2024 Page 1 arXiv:2405.11174v1 [math.CO] 18 May
2024 REFINED DIAMETER BOUNDS UNDER CURVATURE DIMENSION CONDITIONS YI C …