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334 papers · 1 filter
A short proof of a perturbation inequality for the spectral radius
Lele Liu, Bo Ning
Let be a simple graph, and denote by its spectral radius. Sun and Das (2020) established that for any non-isolated vertex with degree , \[ λ(G)\leq \sqrt{λ(G-v…
MacMahon's operator: A computational framework
Feihu Liu, Guoce Xin
MacMahon introduced partition analysis in his book ``Combinatory Analysis'' as a computational technique for solving problems related to systems of linear Diophantine equations and…
Fractional balanced chromatic number of signed subcubic graphs
Xiaolan Hu, Luis Kuffner, Jiaao Li +4
A signed graph is a pair , where is a graph and , called signature, is an assignment of signs to the edges. Given a signed graph wit…
A Note on Weak Saturation Number of Trees
Wenchong Chen, Xiao-Chuan Liu, Xu Yang
In this paper, we estimate the weak saturation numbers of trees. As a case study, we examine caterpillars and obtain several tight estimates. In particular, this implies that for a…
On decycling and forest numbers of Cartesian products of trees
Ali Ghalavand, Sandi Klavžar, Ning Yang
The decycling number of a graph is the minimum number of vertices that must be removed to eliminate all cycles in . The forest number is the maximum numbe…
Zero-one dual characters of flagged Weyl modules
Peter L. Guo, Zhuowei Lin, Simon C. Y. Peng
We prove a criterion of when the dual character of the flagged Weyl module associated to a diagram in the grid is zero-one, that is, the coefficients…