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Let $0 < A < 1$ and $G$ be connected d-regular graph with degree $d=[A n]$. The density of $G$ is about $A$. Q1 Are there constraints on $A$ such that finding maximum independent set of $G$ is ...

One nice identity is that $$\operatorname{tr}(A^3)/6$$ counts the number of triangles of a graph with adjacency matrix $A$. It also implies that triangle counting in a graph can be performed in sub-...

Generally speaking, finding a Hamiltonian cycle is NP-Hard and so tough. But if $G=L(H)$ is the line graph of $H$, then we can reduce the problem of finding a Hamiltonian cycle in $G$ to finding an ...

I'm curious whether the problem below is NP-complete. I provide two simple definitions and one example at first. Definition 1. Let $\langle \cal S_i\rangle\substack{i\in I}$ and $\langle \cal S_j \...

I'm reading the following paper on universality considerations in VLSI circuits http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf In Theorem 2 On the second page it states there exists ...

We got a reduction graph isomorphism to MIS in a very dense graph, or alternatively negative monotone 2-CNF to MAX-ONEs with a formula with many clauses. Let $G,H$ be graphs of order $n$ and adjacency ...