All Questions
15 questions
1
vote
1
answer
45
views
Graph classes which have small edge k-cuts
I am interested in graph classes that have the following property: There exists a function $f(k)$ such that for every graph $G$ in the class, for every choice of $k$ vertices $v_1, \ldots, v_k$ in the ...
- 526
0
votes
1
answer
2k
views
How does the greedy algorithm for CSES problem collecting numbers work? [closed]
The collecting numbers problem in the CSES problem set has a greedy solution where we compare the position of a number x with the position of x-1. If pos(x) < pos(x-1) then we increment rounds ...
- 101
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
7
votes
3
answers
500
views
Minimum number of swaps needed to 'group' a sequence?
Let a finite sequence $s=\{s_1,\dots,s_N\}$ (the characters of which are chosen from a finite set $\{c_1, \cdots, c_M\}$) be called "grouped" if for any $s_i=s_j$, $i<j$, we have $s_k=s_i=s_j$ for ...
- 1,216
0
votes
3
answers
1k
views
Given $N$ integers on a circle, how to choose them in pairs to obtain minimum sum?
(Added by YCor 2019 July 7): it has been mentioned in the comments that this is part of a contest "Circular merging, July Challenge 2019 Division 1", where an equivalent question (just more clearly ...
user142755
64
votes
1
answer
5k
views
How to be rigorous about combinatorial algorithms?
1. The question
This may be the worst question I've ever posed on MathOverflow: broad,
open-ended and likely to produce heat. Yet, I think any progress that will be
made here will be extremely useful ...
- 33.8k
1
vote
1
answer
347
views
Finding a subgraph of cliques with the minimum total sum weight
Consider the following graph problem. For a number $K$ and a set $\mathcal{K} = \{ 1, \ldots,K\}$, we have a set of vertices $V_k^s$ for all $s \subset \mathcal{K} \setminus \{k\}$, $s$ is not empty ...
- 113
5
votes
1
answer
275
views
How to generate $n$ FP32 rationals s.t. no two distinct k-el. subsets have same sum?
First some
Background: I have lots and lots of integer matrices, whose rows are $k$-combinations (without repetitions and sorted) of numbers from the set $S:=\{1,...,n\}$ and needed to be compared ...
- 7,127
4
votes
0
answers
209
views
Rough structure of the double coset space/Graph bijections up to automorphisms
I am dealing with bijective maps $\pi:\Gamma_1\to \Gamma_2$ between two graphs with the same number of vertices $N=O(10)$.
The graphs have a significant automorphism group (these are disconnected ...
- 679
3
votes
1
answer
1k
views
#P version of SUBSET SUM
The decision version of the SUBSET SUM problem asks the following: Given a set of integers $S =$ {$a_1, ..., a_n$}, is there a subset $S'$ of $S$ such that the sum of the elements in $S'$ is equal to ...
22
votes
9
answers
17k
views
Fast evaluation of polynomials
Hello everybody !
I was reading a book on geometry which taught me that one could compute the volume of a simplex through the determinant of a matrix, and I thought (I'm becoming a worse computer ...
- 1,654
5
votes
1
answer
362
views
Drawing graphs on circles
Please consider the following problem:
Given: a simple graph (without self-loops and without multiple edges) $G$ on $n$ vertices.
Task: place equidistantly the vertices of $G$ on a circle of unit ...
user3409
30
votes
1
answer
3k
views
An edge partitioning problem on cubic graphs
Hello everyone,
I already asked this question on the TCS Stack Exchange, but it has not been resolved yet. Maybe readers of this forum will have other ideas or information, although I suspect that ...
- 1,164
3
votes
4
answers
2k
views
Enumerative algorithm through inclusion-exclusion
Hello everybody !
I wondered, without really knowing where to search, whether there was a "smart" way to enumerate/iterate over all the elements of a set which can be counted by inclusion-exclusion. ...
- 1,654
7
votes
1
answer
805
views
Counting Eulerian Orientation in a 4-regular undirected graph
We would like to know how hard it is to count Eulerian orientation in an undirected 4-regular graph. For a given edge orientation to be Eulerian, we mean that every vertex has 2 in-edges and 2 out-...
