All Questions
12 questions
44
votes
4
answers
5k
views
Why is "P vs. NP" necessarily relevant?
I want to start out by giving two examples:
Graham's problem is to decide whether a given edge-coloring (with two colors) of the complete graph on vertices $\lbrace-1,+1\rbrace^n$ contains a planar $...
- 25.5k
10
votes
3
answers
1k
views
Is there a website or a survey collecting all NP-complete problems on graph theory?
I wonder whether there is a website or a survey collecting all known NP-complete or NP-hard problems on graph theory?
- 557
6
votes
0
answers
1k
views
Is Logical Min-Cut Problem, NP-Complete? [closed]
Logical Min Cut (LMC) Problem: Suppose that G = (V, E) is an unweighted digraph, s,t are two vertices of V, and t is reachable from s. LMC Problem states that how we can make t unreachable from s by ...
- 161
3
votes
0
answers
56
views
Karp hardness of two cycles which lengths differ by one
Our problem is as follows:
NEARLY-EQUAL-CYCLE-PAIR
Input: An undirected graph $G(V,E)$
Output: YES if there exists $2$ (simple) cycles in $G$ which lengths differ by $1$, otherwise NO
Is it $NP$-...
- 121
2
votes
3
answers
184
views
Reference Request for: Finding Large Bipartite Subgraphs via Destruction of Odd Cycles in Graphs
From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...
- 13.2k
2
votes
2
answers
553
views
Need input on a potentially NP-hard maximal edge-weighted multi-cycle graph
I've posted a question on Stack Overflow regarding a seemingly NP-hard problem on maximization of weighted cycles in a graph problem.
One of the respondents cited Professor David Speyer's Math ...
- 21
2
votes
1
answer
120
views
$W[1]$-hard and FPT about the equitable tree-coloring problem
I am confused by the two conclusions in this paper (DOI link behind paywall at Springerlink).
It shows that the equitable tree-coloring problem is $W[1]$-hard when parameterized
by treewidth.
However, ...
- 91
2
votes
1
answer
978
views
Is undirected short-simple-path-through-3-vertices decidable in polynomial time?
Consider the following language:
$L=\{\langle G=(V,E),s,v,t,l\rangle\;|\;s,v,t\in V, l\in \mathbb{N} \wedge $ There exists a simple path from $s$ to $t$, going through $v$ of length $\leq l\}$.
($G$ ...
- 618
1
vote
3
answers
267
views
Strategic vertex labeling
We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled 0(all vertices with ...
- 113
1
vote
0
answers
78
views
Bipartite clustering is NP-hard?
Let $G = (A\cup B, E)$ be a bipartite graph with edge weights $w: E\to \mathbb{R}$. Find a partition $B_1, B_2$ of $B$ and a nonempty disjoint subsets $A_1, A_2$ of $A$ such that $w(A_1,B_1) + w(A_2, ...
- 221
0
votes
0
answers
16
views
Complexity of finding single source paths with capacity constraints and length constraints
Let $G=(V,A)$ be a directed graph with distinguished vertex $s\in V$ and let $c:A\rightarrow{\mathbb N}$ denote arc capacities. For any $t\in V,t\not=s$ we are given two numbers: $C_{t},L_{t}$. Let $...
- 21
0
votes
2
answers
251
views
Compute the average path weights of paths with the same path length in a directed acyclic graph (DAG)
Given a weighted directed acyclic graph (DAG) $G=(V,E)$ with each edge $e\in E$ has a non-negative weight $w(e)$. For a path $p=(e_1,e_2,\dotsc,e_n)$ in $G$, define the path weight as : $w(p)=\sum_{i=...
- 143