The standard graded property for vertex cover algebras of Quasi-Trees

TL;DR

This paper provides a combinatorial criterion to determine when vertex cover algebras of quasi-trees are standard graded, including an example and computation of the maximal degree of minimal generators.

Contribution

It introduces a simple combinatorial criterion for the standard graded property of vertex cover algebras of quasi-trees, expanding prior characterizations.

Findings

The criterion effectively determines the standard graded property.

An explicit example demonstrates the criterion's application.

The maximal degree of minimal generators is computed in the example.

Abstract

J. Herzog, T. Hibi, N. V. Trung and X. Zheng characterize the vertex cover algebras which are standard graded. In this paper we give a simple combinatorial criterion for the standard graded property of vertex cover algebras in the case of quasi-trees. We also give an example of how this criterion works and compute the maximal degree of a minimal generator in that case.