All Questions

$\DeclareMathOperator\cl{cl}$The cyclic edge connectivity $\cl(G)$ is the size of a smallest cyclic edge cut, i.e., a smallest edge cut $F$ such that $G-F$ has two connected components, each of which ...

The problem of finding a k-edge connected spanning subgraph with the minimum number of edges is $ \mathcal{NP} $-hard in general. Is it the case for positive weighted graphs with "fractional ...

Given an undirected graph $G=(V,E)$, the max-cut problem asks for the partition $S_1,S_2\subset V$ , s.t., the number of edges going from $S_1$ to $S_2$ are maximized. Is it possible to maximize the ...

It is known that a graph $G=(V,E)$ with $n$ nodes and min cut $k$, must have at least $\frac{1}{2}nk$ edges. Are there any tighter bounds or expectations I can place on $|E|$ if I assume that $G$ ...

Given a single-component, directed acyclic graph with one source (vertex with only outgoing edges) and one sink (vertex with only incoming edges), I'd like to find a minimum spanning subgraph which ...

I am looking for examples/families of graphs with the following (maybe vague-sounding at first) property: the graph $G$ has a relatively large subgraph $B$ such that $B$ is bipartite-plus-a-few-edges ...