Questions tagged [bounded-degree]
The bounded-degree tag has no usage guidance.
9
votes
1answer
188 views
Finding subgraphs with high treewidth and constant degree
I am given a graph $G$ with treewidth $k$ and arbitrary degree, and I would like to find a subgraph $H$ of $G$ (not necessarily an induced subgraph) such that $H$ has constant degree and its treewidth ...
6
votes
0answers
174 views
Bias of a random boolean low degree polynomial
What is the bias of a random Boolean function that can be represented as a low degree polynomial over the reals, i.e. has low Fourier degree?
More specifically, is it true that if we take a uniformly ...
5
votes
1answer
286 views
Degree restriction for polynomials in $\mathsf{VP}$
why do we need the restriction on the degree for a polynomial to be in VP due to which $(\prod_{i=0}^{n} x_i)^{2^n}$ $\notin$ VP even though it has a poly-size circuit?
21
votes
1answer
353 views
Random functions of low degree as a real polynomial
Is there a (reasonable) way to sample a uniformly random boolean function $f:\{0,1\}^n \to \{0,1\}$ whose degree as a real polynomial is at most $d$?
EDIT: Nisan and Szegedy have shown that a ...
12
votes
4answers
1k views
hardness of approximating the chromatic number in graphs with bounded degree
I am looking for hardness results on vertex coloring of graphs with bounded degree.
Given a graph $G(V,E)$, we know that for any $\epsilon>0$, it's hard to approximate $\chi(G)$ within a factor ...
3
votes
1answer
167 views
bounded outdegree bipartite spanners
Given an undirected graph $G = (V,E)$ and an integer $k > 0$, our objective is to find a subgraph $G' = (V ,E')$ where $E' \subseteq E$ such that $G'$ has the three following properties :
$G'$ ...
19
votes
2answers
869 views
Is feedback vertex set problem is solvable in polynomial time for 3-degree bounded graphs?
Feedback Vertex Set is NP-complete for general graphs. It is known to be NP-complete for degree-8 bounded graphs due to a reduction from vertex cover.
The Wikipedia article says that it is poly-time ...
1
vote
2answers
212 views
Complexity of finding if a degree bounded graph H is a subgraph of an unbounded graph G
You are given two graphs G and H , and want to know if H is a subgraph of G.
You know that H has a max vertex degree K (constant integer).
What can you say about the complexity of this?
I know that ...
10
votes
1answer
356 views
Hardness of approximating fractional chromatic number on bounded degree graphs
Is it apx-hard to approximate fractional chromatic number on bounded degree graphs?
