# Questions tagged [graph-theory]

Graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects.

1,404 questions
Filter by
Sorted by
Tagged with
228 views

### 3-colourability of Eulerian maximal planar graph

The following paragraph is from this answer by David Eppstein (emphasis mine). A maximal planar graph is 3-colorable iff it is Eulerian (if it is not Eulerian, then the odd wheel surrounding a single ...
117 views

113 views

### Intuition behind the Charikar's LP formulation for densest subgraph problem

I understand why the LP gives the optimal solution for the densest subgraph problem. But don't understand the intuition behind the LP in this paper. Just mentioning the LP for maximum density of a ...
160 views

### Tree decompositions of optimal width where every vertex is in a bounded number of bags?

Let $G$ be a graph on $n$ vertices whose maximum degree is at most $\Delta$ and whose treewidth is at most $k$. Does there exist a function $f(k, \Delta)$, independent of $n$, such that it is possible ...
754 views

### Algorithm for finding a 3-cycle cover

Given: An undirected, unweighted graph Looking for: A disjoint vertex cycle cover where every cycle has at least 3 edges Is there any algorithm that solves this problem, possibly with some ...
110 views

### Network design with reachability pattern

We are given two sets of terminals $A$ and $B$. For each $a\in A$, we are also given $R_a\subseteq B$. Let $|A|+|B|=n$. We want to find a directed acyclic graph $G$ where $A$ and $B$ are subsets of ...
314 views

### Is the maximum independent set in cubic planar graphs NP-complete?

In their famous book, Garey and Johnson, write a comment that the maximum independent set problem, in cubic planar graphs is NP-complete(page 194 of the book). They say this is by a transformation ...
144 views

### How to efficiently find a loop between two nodes in a directed graph?

Given two nodes in a directed graph, how can I find a loop (if exists) that pass these two nodes? The loop cannot pass a node more than once. And if there isn't such a loop, how to efficiently ...
120 views

52 views

### When can partial spectral sparsifiers be combined?

A few important papers about spectral sparsifiers and friends contain a technical idea that involves building many different sparsifiers that each "partially" solve the problem, and then combining ...
149 views

### List of NP-Complete graph problems/ properties?

Is there a good source to find various decision problems on graph and networks? For a project I'm doing it'd be useful to be able to look at lots of different problems. Is there a good source for ...