All Questions
Tagged with algorithms random-graphs
9 questions
2
votes
1
answer
211
views
The complexity of expansion ratio (Cheeger constant) of a graph
Let $G=(V(G), E(G))$ be a graph on $n$ vertices and let $S$ be a subset of $V(G)$. The boundary of $S$, denoted by $\partial S$, is the set of edges $(i, j)$ such that $i \in S$ and $j \in V(G) \...
- 640
3
votes
0
answers
107
views
Random graphs with prescibed degrees and triangles
In short: a random graph model generates (multi-)graphs with prescribed number of edges and minimal number of triangles for each vertex. Questions arise about the actual number of triangles and the ...
- 1,444
2
votes
0
answers
69
views
Are two degree sequences compatible, for random simple graph generation?
Consider a set $V$ of $n$ vertices, and three degree sequences $a_i$, $b_i$ and $c_i$ such that $c_i = a_i+b_i$, $i=1..n$.
Assume these degree sequences are graphical: there exist simple graphs (no ...
- 1,444
5
votes
3
answers
411
views
Simple graphs with prescribed degrees as disjoint union of simple subgraphs with prescribed degrees
Consider a set $V$ of $n$ vertices, and three degree sequences $a_i$, $b_i$ and $c_i$ such that $c_i = a_i+b_i$, $i=1..n$.
Assume these degree sequences are graphical: there exist simple graphs (no ...
- 1,444
5
votes
2
answers
265
views
Triangle coloring in random graph
Given $m$ persons (men and women) and $n$ balls, each person randomly selects $3$ balls. Once all of them complete the selection process, we color the balls with $2$ colors, white and black, such that ...
- 367
186
votes
3
answers
96k
views
Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on applications?
QUICK FINAL UPDATE: Just wanted to thank you MO users for all your support. Special thanks for the fast answers, I've accepted first one, appreciated the clarity it gave me. I've updated my torus ...
- 343
4
votes
2
answers
207
views
Fast uniform generation of random graphs with given degree sequences - any implementation?
The paper below presents a linear-time algorithm for uniform generation of random graphs with given degree sequences [1].
This is very interesting in practice, but I found no implementation. However, ...
- 1,444
4
votes
0
answers
220
views
Navigation in a graph
The problem
Let $G=(V,E)$ be a graph. $k = O\left(\log(|V|)\right)$ distinct vertices are picked randomly from $V$. We call the set of chosen $k$ vertices $T$.
Assumptions about the graph: You may ...
- 323
8
votes
1
answer
630
views
Change in the average geodesic distance of a graph when flipping a single edge
Is there a way to determine how the average geodesic distance between nodes of a graph will change just by flipping (1) a single edge without having to traverse the whole graph like in the Djikstra ...
- 923