5
votes
1answer
112 views

Is Hamiltonian path NP-hard on graphs of diameter 2?

Let $G$ be a graph of diameter 2 ($\forall u,v\in V: d(u,v)\leq2$). Can we decide if $G$ has Hamiltonian path in poly time? What about digraphs? Perhaps some motivation is in place: the ...
1
vote
1answer
35 views

Is the minimum weight independent dominating set np-complete in chordal graphs?

I have a found a small article [1] saying (the first paragraph of the introduction) that the minimum-weight independent dominating set is NP-complete in chordal graphs, but at the same time, seems to ...
2
votes
3answers
1k views

Proof that the existence of a Hamilton Path in a bipartite graph is NP-complete

I tried to solve the above NP-completeness exercise by making a bipartite graph from a general one (undirected) by inserting a vertice in the middle of every edge of the first (general) graph. This ...
10
votes
3answers
266 views

Minimal size of contracting a DAG into a new DAG

We have a DAG. We have a function on the nodes $F\colon V\to \mathbb N$ (loosely speaking, we number the nodes). We would like to create a new directed graph with these rules: Only nodes with the ...
4
votes
1answer
53 views

Max cut in cubic graphs

The following question is related to the max cut problem in cubic graphs. In this survey paper Theorem 6.5 states A maximal cut of a cubic graph can be computed in polynomial time Browsing ...
4
votes
1answer
151 views

Is “Find the shortest tour from a to z passing each node once in a directed graph” NP-complete?

Given a directed graph with the following attributes: - a chain from node $a$ to node $z$ passing nodes $b$ to $y$ exists and is unidirectional. - additionally a set of nodes having bidirectional ...
-1
votes
1answer
128 views

Reducing from Hamiltonian Cycle problem to the Graph Wheel problem cannot be proved vice versa [closed]

I saw a proof by Saeed Amiri, We will add one extra vertex v to the graph G and we make new graph G′, such that v is connected to the all other vertices of G. G has a Hamiltonian cycle if and only if ...
2
votes
1answer
98 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. The problem is to ...
-1
votes
2answers
161 views

Wheel subgraph problem [duplicate]

In the following two threads I specified the question in the wrong way (easier to solve that way). Proving that finding wheel subgraphs is NP-complete Reducing from Hamiltonian Cycle problem to the ...
2
votes
1answer
985 views

Reduction from Vertex Cover to an Independent Set problem

Assume there exists some algorithm that solves vertex cover problem in time polynomial in terms of $n$ and exponential for $k$ with the run time that looks like this $O(k^2 55^k n^3)$. Can we claim ...
0
votes
1answer
119 views

Reduction from 3-SAT to a graphe problem

I have a question, i was trying to reduce 3-SAT to a particular graph problem and i'm not quite sure about a thing i used in the reduction. In fact the reduction build a bipartite graph, the edge ...
1
vote
2answers
193 views

Proving that finding wheel subgraphs is NP-complete

Can you help me with this problem ? Given an undirected graph $G$ and an integer $n$, prove that determining whether the graph has wheel on $n$ vertices $W_{n}$ (a wheel $W_{i}$ is such that $i$ ...
7
votes
1answer
242 views

For what special cases does this vertex cover algorithm fail or work?

I'm trying to find a polynomial time algorithm for finding the minimum vertex cover for a graph. I've written the algorithm below; I know this problem is $\mathsf{NP}$-hard, which means there are ...
3
votes
2answers
446 views

Is the clique problem NP-complete also on bipartite or planar graphs?

We know that the clique problem is NP-complete. Is the restriction of the problem to bipartite graphs or planar graphs still NP-complete?
4
votes
1answer
100 views

Vertex coloring with an upper bound on the degree of the nodes

Consider the set of graphs in which the maximum degree of the vertices is a constant number $\Delta$ independent of the number of vertices. Is the vertex coloring problem (that is, color the vertices ...
4
votes
1answer
277 views

NP-completeness of graph isomorphism through edge contractions with an edge validity condition

Given Graphs $G=(V_1,E_1)$ and $H=(V_2,E_2)$. Can a graph isomorphic to $H$ be obtained from $G$ by a sequence of edge contractions ? We know this problem is NP-complete. What about if only a subset ...
4
votes
0answers
113 views

Proof of NP-completeness of graph isomorphism through edge contractions that reduce a metric [duplicate]

Duplicate: NP-completeness of graph isomorphism through edge contractions with an edge validity condition I know that graph contractability is $NP$-complete. To be specific given ...
9
votes
2answers
679 views

NP-Completeness of a Graph Coloring Problem

Alternative Formulation I came up with an alternative formulation to the below problem. The alternative formulation is actually a special case of the problem bellow and uses bipartite graphs to ...
14
votes
1answer
1k views

NP completeness proof of a spanning tree problem

I am looking for some hints in a question asked by my instructor. So I just figured out this decision problem is $\sf{NP\text{-}complete}$: In a graph $G$, is there a spanning tree in $G$ that ...