DICHROMATIC NUMBER AND FRACTIONAL CHROMATIC NUMBER

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Dichromatic Number and Fractional Chromatic Number

The dichromatic number of a graph G is the maximum integer k such that there exists an orientation of the edges of G such that for every partition of the vertices into fewer than k parts, at least one of the parts must contain a directed cycle under this orientation. In 1979, Erdős and NeumannLara conjectured that if the dichromatic number of a graph is bounded, so is its chromatic number. We m...

متن کامل

The fractional chromatic number of the plane

The chromatic number of the plane is the chromatic number of the uncountably infinite graph that has as its vertices the points of the plane and has an edge between two points if their distance is 1. This chromatic number is denoted χ(R). The problem was introduced in 1950, and shortly thereafter it was proved that 4 ≤ χ(R) ≤ 7. These bounds are both easy to prove, but after more than 60 years ...

متن کامل

The fractional chromatic number of mycielski's graphs

The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G n of triangle-free graphs with (G n ) = n. In this note, we calculate the fractional chromatic number of G n and show that this sequence of numbers satis es the unexpected recurrence a n+1 = a n + 1 a n .

متن کامل

More results on r-inflated graphs: Arboricity, thickness, chromatic number and fractional chromatic number

The r-inflation of a graph G is the lexicographic product G with Kr. A graph is said to have thickness t if its edges can be partitioned into t sets, each of which induces a planar graph, and t is smallest possible. In the setting of the r-inflation of planar graphs, we investigate the generalization of Ringel’s famous Earth-Moon problem: What is the largest chromatic number of any thickness-t ...

متن کامل

Fractional chromatic number and circular chromatic number for distance graphs with large clique size

Let Z be the set of all integers and M a set of positive integers. The distance graph G(Z,M) generated by M is the graph with vertex set Z and in which i and j are adjacent whenever |i − j| ∈ M . Supported in part by the National Science Foundation under grant DMS 9805945. Supported in part by the National Science Council, R. O. C., under grant NSC892115-M-110-012.

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: Forum of Mathematics, Sigma

سال: 2016

ISSN: 2050-5094

DOI: 10.1017/fms.2016.28