# Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

229 questions with no upvoted or accepted answers
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### Connected Components over Graph with “colored” edges.

We have an undirected graph $G(V,E)$. Each edge $e \in E$ is associated with a set $C_{e}\neq \emptyset$ of colors, $C_{e} \subseteq C$. The problem is to find all the colored connected components. ...
118 views

### Are local canonical labellings of a graph ever a subsequence of the global canonical labelling?

So a canonical labelling of a graph G is a function CL(G) that maps each vertex to a numerical label. Sorry if my definitions are a bit obvious or clumsy, by the way. For every isomorphic graph G', CL(...
425 views

### Optimization Problem on a Directed Graph

I have the following graph optimization problem. In a directed graph $G$, each node $i$ is endowed with a real value $v_i$ (input) that encodes the minimum "activation threshold" of that node. For ...
76 views

### Variation of edge-disjoint spanning trees

In a directed graph, I want to find 2 edge-disjoint spanning trees (arborescence), with the extra restrictions that edges in the 1st tree are not forward arcs in the 2nd tree. Are there existing ...
94 views

### How to approach the “traveling salesman problem” with cost changing every time salesman reaches a new city

Let's say instead of finding the shortest path we have to maximize the profit in a year of the salesman under the following constraints. Salesman can go to a different city only on weekends, all ...
47 views

### Efficient game traversal of a DAG of 3-colorings

Let $X$ be a set of size $n$. Consider a game played on board $X$ by two players black and white. Starting with the empty board, each player chooses an empty spot to place a stone. Black moves ...
78 views

### Algorithm for computing the smallest subset of nodes to remove from a graph to make it a tree

I have encountered an interesting problem that I couldn't find any references to solve: Determine the smallest subset of nodes that need to be removed from an undirected graph to make it a tree. ...
86 views

### Common techniques for the acyclic orientation problem under some special constraint?

An acyclic orientation of an undirected graph is an assignment of a direction to each edge(an orientation) that does not form any directed cycle and therefore generates a directed acyclic graph(DAG). ...
142 views

### Shortest s-t path when is allowed to ignore k weights

Given an undirected graph $G$ with $n$ vertices and $m$ edges, with non-negative weights on the edges, what's the best algorithm that computes the shortest path from $s$ to $t$, where you are allowed ...
136 views

### Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
108 views

### Counting the maximum number of paths of length $n$ that differ in at least $k$ edges

What is known about the complexity of solving (or approximately solving) the following problem? INPUT: Graph $G=(V,E)$ and constants $L$ and $K$. OUTPUT: The maximum size of any set $S$ of simple ...