منابع مشابه
Spatial Mixing of Coloring Random Graphs
We study the strong spatial mixing (decay of correlation) property of proper q-colorings of random graphG(n, d/n) with a fixed d. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as G(n, d/n), an easy counterexample shows that colorings do not exh...
متن کاملEdge-coloring Vertex-weightings of Graphs
Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...
متن کاملStrong spatial mixing for list coloring of graphs
The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise known to be #P hard. In the context of coloring, strong spatial mixing has been established for regular trees in [GS11] when q ≥ α∗∆+ 1 where q the number o...
متن کاملSub-coloring and Hypo-coloring Interval Graphs
In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as “subroutines” for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color clas...
متن کاملColoring Semirandom Graphs
We study semirandom k-colorable graphs made up as follows. Partition the vertex set V = {1, . . . , n} randomly into k classes V1, . . . , Vk of equal size and include each Vi-Vj -edge with probability p independently (1 ≤ i < j ≤ k) to obtain a graph G0. Then, an adversary may add further Vi-Vj-edges (i 6= j) to G0, thereby completing the semirandom graph G = G∗n,p,k . We show that if np ≥ max...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2001
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216501000755