The inertia bound and ratio bound (also known as the Cvetković bound and Hoffman bound)
are two fundamental inequalities in spectral graph theory, giving upper bounds on the …

A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal
vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a …

Chung et al. constructed an induced subgraph of the hypercube Q n Q^n with α (Q n)+ 1
α(Q^n)+1 vertices and with maximum degree smaller than⌈ n⌉ ⌈n⌉. Subsequently, Huang …

The study of complexity measures of Boolean functions led Nisan and Szegedy to state the
sensitivity conjecture in 1994, claiming a polynomial relation between degree and …

Abstract Hao Huang proved the Sensitivity Conjecture in [Induced graphs of the hypercube
and a proof of the Sensitivity Conjecture, Annals of Mathematics, 190 (2019), 949-955] by …

In this paper, we consider induced subgraphs of the Hamming graph $ H (n, 3) $. We show
that if $ U\subseteq\mathbb {Z} _3^ n $ and $ U $ induces a subgraph of $ H (n, 3) $ with …

The semi-strong product of graphs G and H is a way of forming a new graph from the graphs
G and H. The vertex set of the semi-strong product is the Cartesian product of the vertex sets …

We study the maximum degree of large induced subgraphs of some highly symmetric
graphs. This type of problem for Boolean hypercubes was formulated as an equivalent …

This thesis addresses the extent of the covering graph construction. How much must a cover
X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics …

Graph theory is the mathematics of networks. This thesis develops novel techniques to
understand the structure of graphs in both the sparse and dense regimes. These techniques …