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Questions about graphs, discrete structures of nodes which are connected by edges, including trees and graphs with weighted edges.

3 votes
Accepted

Basic questions about network flow calculations

I think all your questions are answered by examining the actual algorithm to compute the max flow. With regards to your Q1: in the max flow problem your input is a graph and capacities on edges, your …
Denis Pankratov's user avatar
2 votes

How many $(x, y)$-paths of length $20$ are there, where $x$, $y$ adjacent vertices in cycle ...

Hint: consider powers of adjacency matrix of $C_5$ (Wiki: Matrix powers).
Denis Pankratov's user avatar
13 votes
Accepted

Linear-time algorithm to find an odd-length cycle in a directed graph

Let $G$ be strongly connected. Run BFS (!) from an arbitrary vertex $s$. BFS creates a leveled tree where level of a vertex $v$ is it's directed distance from $s$. If while running BFS you have never …
Denis Pankratov's user avatar