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Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

10
votes
1answer
A graph $G$ is chordal if it doesn't have induced cycles of length $4$ or more. A clique tree $T$ of $G$ is a tree in which the vertices of the tree are the maximal cliques of $G$. An edge in $T$ corr …
asked Apr 2 '13 by Juho
6
votes
1answer
Given an adjacency matrix $A_G$ of an undirected graph $G$, it is easy and straightforward to compute the characteristic polynomial $\chi_G(\lambda)$. What about the other way around? The problem can …
asked Oct 16 '12 by Juho
6
votes
1answer
A graph $G$ is chordal if it doesn't have induced cycles of length 4 or more. Chordal graphs are precisely the class of graphs that admit a clique tree representation. A clique tree $T$ of $G$ is a tr …
asked Mar 10 '13 by Juho
14
votes
2answers
Let $G$ be a graph, and let $s$ and $t$ be two vertices of $G$. Can we efficiently sample a shortest $s$-$t$ path uniformly and independently at random from the set of all shortest paths between $s$ a …
asked Nov 11 '13 by Juho
3
votes
1answer
We are given a labelled directed graph, where both vertices (or states) and edges (or transitions) have labels. Informally, two states are bisimilar when they have the same label and they can simulate …
asked Nov 15 '12 by Juho