Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 24 November 2020Accepted: 25 July 2021Published online: 23 2021Keywordsgraphs, fractional coloring, girth, triangle-free, RamseyAMS Subject Headings05C15Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied Mathematic...

The average distance of a vertex $v$ connected graph $G$ is the arithmetic mean distances from to all other vertices $G$. proximity $\pi(G)$ and remoteness $\rho(G)$ are minimum maximum $G$, respectively. In this paper, we give upper bounds on for graphs given order, degree degree. Our sharp apart an additive constant.

With any surjective rational map \(f: \mathbb {P}^n \dashrightarrow {P}^n\) of the projective space, we associate a numerical invariant (ML degree) and compute it in terms naturally defined vector bundle \(E_f \longrightarrow {P}^n\).

The star valency of a graph G is the minimum, over all star decompositions , of the maximum number of elements in incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either dmax-ave(G)=2 or dmax-ave(G)=2 +1, and provide a polynomial time algorithm for determini...

This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a O(D̄ log log D̄/ log D̄) bound, where D̄ is the average weighted degree in a hypergraph, matching the best bounds known for the sp...

The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices. These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the latti...