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Results tagged with graph-theory
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user 82949
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
2
votes
0
answers
252
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maximum independent set in d-regular graphs
Does anyone know whether the maximum independent set problem is NP-hard in triangle free d-regular graphs and if it's NP-hard for all d larger than some threshold t? Can anyone provide a reference als …
- 213
1
vote
0
answers
34
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Some confusion regarding the definition of NPO reduction
I've seen the following definition in a paper on approximation preserving reductions.
Definition:Let $\pi_{1}$ and $\pi_{2}$ be two NPO maximization problems. Then we say that $\pi_{1} \leq_{R} \pi_{ …
- 213
3
votes
2
answers
352
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Sparse graphs that are hard to color
I am interested in knowing if there are any types of graphs that are very sparse, perhaps consisting of just connections between paths and cycles, and for which $k$-coloring is $\mathsf{NP}$-hard for …
- 213
5
votes
2
answers
408
views
An interesting variant on the maximum independent set problem.
Suppose i have a graph $G=(V,E)$ with $|V|=n$. Furthermore suppose i give you a maximum independent set $\mathcal{I}$ in $G$. Now suppose i obtain a new graph $G'$ from $G$ by removing a single vertex …
- 213