21 citations · 49 across the 16 of their papers we have counts for
7 papers · 1 filter
Counting substructures and eigenvalues II: quadrilaterals
Bo Ning, Mingqing Zhai
Let be a graph and be the spectral radius of . A previous result due to Nikiforov [Linear Algebra Appl., 2009] in spectral graph theory asserted that every graph …
Counting substructures and eigenvalues I: triangles
Bo Ning, Mingqing Zhai
Motivated by the counting results for color-critical subgraphs by Mubayi [Adv. Math., 2010], we study the phenomenon behind Mubayi's theorem from a spectral perspective and start u…
Outerplanar Turán numbers of cycles and paths
Longfei Fang, Mingqing Zhai
A graph is outerplanar if it can be embedded in a plane such that all vertices lie on its outer face. The outerplanar Turán number of a given graph , denoted by ${\rm ex}_{\math…
Spectral radius, edge-disjoint cycles and cycles of the same length
Huiqiu Lin, Mingqing Zhai, Yanhua Zhao
In this paper, we give spectral conditions to guarantee the existence of two edge disjoint cycles and two cycles of the same length. These two results can be seen as spectral analo…
Spectral extrema of -minor free graphs--On a conjecture of M. Tait
Mingqing Zhai, Huiqiu Lin
Minors play an important role in extremal graph theory and spectral extremal graph theory. Tait [The Colin de Verdière parameter, excluded minors, and the spectral radius, J. Combi…
Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs
Mingqing Zhai, Huiqiu Lin, Jinlong Shu
Nikiforov [Some inequalities for the largest eigenvalue of a graph, Combin. Probab. Comput. 179--189] showed that if is -free then the spectral radius $ρ(G)\leq\sqrt{2…
A strengthening of the spectral chromatic critical edge theorem: books and theta graphs
Mingqing Zhai, Huiqiu Lin
The chromatic critical edge theorem of Simonovits states that for a given color critical graph with , there exists an such that the Turán graph is…