Randomly coloring constant degree graphs

نویسندگان
چکیده

منابع مشابه

Randomly coloring graphs of logarithmically bounded pathwidth

We consider the problem of sampling a proper k-coloring of a graph of maximal degree ∆ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of logarithmically bounded pathwidth if k ≥ (1+ )∆, for any > 0, using a new hybrid paths argument. ∗California Institute of Technology, Pasadena, CA, 91125, USA. E-mail: [email protected].

متن کامل

Randomly coloring graphs of bounded treewidth

We consider the problem of sampling a proper k-coloring of a graph of maximal degree ∆ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if k ≥ (1 + )∆, for any > 0.

متن کامل

Randomly coloring sparse random graphs with fewer colors than the maximum degree

We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree log n/ log log n, with high probability. We efficiently generate a random k-coloring when k = Ω(log log n/ log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold for a more general class of graphs, but...

متن کامل

Partitioning and coloring graphs with degree constraints

We prove that if G is a vertex-critical graph with χ(G) ≥ ∆(G) + 1 − p ≥ 4 for some p ∈ N and ω(H(G)) ≤ χ(G)+1 p+1 − 2, then G = Kχ(G) or G = O5. Here H(G) is the subgraph of G induced on the vertices of degree at least χ(G). This simplifies the proofs and improves the results in the paper of Kostochka, Rabern and Stiebitz [8].

متن کامل

Edge coloring regular graphs of high degree

We discuss the following conjecture: If G = (V; E) is a-regular simple graph with an even number of vertices at most 22 then G is edge colorable. In this paper we show that the conjecture is true for large graphs if jV j < (2 ?)). We discuss related results.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Random Structures & Algorithms

سال: 2012

ISSN: 1042-9832

DOI: 10.1002/rsa.20451