# Questions tagged [graphs]

For questions related to graphs, a mathematical object consisting of a set of nodes with edges connecting certain pairs of them.

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### Can't understand K-Truss Graph properties

Cross-posted on Mathematics SE. Since I have to implement an algorithm in the language of linear algebra, I'm trying to understand K-Truss Graphs which are defined as such The k-truss is a subset of ...
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### Are N-clubs nested?

An $N$-club is defined as follows:   $U \subseteq V$ in an $N$-club in $G$ if $\operatorname{diam}(G[U]) \leq N$. An $N$-club being nested would mean that it contains $N(N-1)$-clubs. My intuition is ...
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### Graph matching with apriori information about the matches?

Given two graphs with n vertices each, where apriori information regarding the similarity of each pair of vertices (between the source and target nodes) is given, is there a known concept for finding ...
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### Reduction from Steiner Tree to TSP

The Steiner Tree version that I am considering is the following: given an undirected weighted graph $G=(V,E)$ and a subset of vertices $T \subseteq V$, find a minimum tree that connects all the ...
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### Heuristic solution to the graph partitioning problem

I am working on a graph partitioning problem. A static column generation based solution was proposed in How to partition a graph with optimal number of groups? But I need some MILP solver to solve ...
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### Numbering the vertices of an $n$-layer graph so that edges have similar numbered vertices on their ends

Consider a graph whose vertices can be partitioned into $n$ layers. Edges exist only between vertices in successive layers. So, there are edges between layers $1$ and $2$, between layers $2$ and $3$ ...
193 views

### Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
154 views

### How to partition a graph with optimal number of groups?

I have a graph with $N=12$ nodes. Some nodes may not have any edge between them. every edge has a weight. How to find the optimal partitioning of the graph so that total weight in the system is ...
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### Quickest shortest path algorithm

I want to do a shortest path algorithm. My direct and not acyclic graph contains only positive numbers. I have to do the scan for all pairs of nodes in complete depth in python. My graph is big (...
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### What is intended when we use "robustness", "resilience" and "reliability" in Operations Research?

I will use an example to detail my question but I would like you to keep in mind that I wanted to define: Robustness, Resillience, Reliability in the most general case within Operations Research. ...
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### What is the name of the graph where any edge is part of a cycle?

I wonder if there is a special category for this kind of graphs, I am thinking of a bidirectional graph but it would also be interesting in the cases when it is undirected. I am thinking of something ...
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### How to find all descendant vertices of all vertices in a big DAG (Directed acyclic graph)?

A simple algorithm may be traverse all vertices, and perform DFS for every vertex. However, the computational complexity is $O(n(n+m))$, where $n$ and $m$ are the number of vertices and edges in the ...
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### Is this a common generalization of the independent set problem?

Suppose a minimum weighted independent set in a conflict graph with $n$ vertices. The basic version is where each vertex $i$ is associated with a weight $c_i$. i.e., there is a vector $C$ for the ...
255 views

### social network analysis - relations between people with weights

I asked this question on datascience.stackexchange but they directed me here. I have a social network represented as a set of people $S$ and individual weights for each of person (weight is the cost ...
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### Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
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### Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
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### Clustering a large ride-matching problem

Background: We are solving a large scale vehicle to person ride-matching problem. The problem is essentially simple (match every person with a vehicle, if possible), yet the problem size is quite ...
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### Covering problem on a network (?)

I have this problem described in natural language, and I was wondering whether it is relatable to any known problem. I have a directed acyclic graph. Each node can host a "probe". If node $i$ hosts ...
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### Maximum Flow Problem : Can someone refer me to accessible valuable resources

Can anyone please refer/suggest me some accessible papers, works, books, websites, documentation related to The Maximum Flow Problem.
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### How to use the least number of colours to colour different routes of a bus route such that no two intersecting routes will have the same colour

I would like to know of a method in which if provided say 10 routes with details regarding which route intersects with which another route, we can use the least number of colours to colour the routes, ...
159 views

### Could DOcplex.CP recognize that it solves the graph coloring minimization problem?

I created a graph coloring DOcplex.CP model inspired by this example. However, I do not know the number of colors in advance. The goal is to minimize the number of colors (i.e., get as close as ...
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### Multiple shipments with FILO order

I am trying to solve a problem statement with the help of jsprit. There is a depot. Identical items need to be delivered or picked up. An item can have two states: Bad or good. Bad items need to be ...
226 views

### Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
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### Network flow model - How can I turn this diagram into a matrix that when converted to RREF solves for max flow?

I have the following network flow model diagram and I have already calculated maximum flow using the R package igraph to be 28. However, what I would like to know ...
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### A variant of the Shortest Path Problem

Consider a layerwise directed acyclic graph DAG, $G=(V,E)$ and two vertices $s$ and $t$. $s$ is connected to all vertices in $L_0$, $L_0$ is connected to all vertices in $L_1$ and so forth. Consider ...
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### A variant of the Multiple Traveling Salesman Problem

I am trying to find a reference (or a reformulation) of a variant of the multiple Traveling Salesman Problem, where multiple agents need to visit each vertex in a graph with minimal cost. Most of the ...
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### References for "metric" network flow problems

Network flow problems are very well studied in the literature (e.g., see the Network Flows book), and the first DIMACS challenge was dedicated to these problems. Very efficient implementation of ...