منابع مشابه
On the Computation and Chromatic Number of Colored Domino Tilings
A colored domino is a rotatable 2× 1 rectangle that is partitioned into two unit squares, which are called faces, each of which is assigned a color. In a colored domino tiling of an orthogonal polygon P , a set of dominoes completely covers P such that no dominoes overlap and so that adjacent faces have the same color. We provide tight bounds on the number of colors required to tile simple and ...
متن کاملThe 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 کاملOn the Chromatic Number of Subsets of the Euclidean Plane
The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is between 4 and 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane such as extensions of the rational pl...
متن کاملAxiom of choice and chromatic number: examples on the plane
In our previous paper (J. Combin. Theory Ser. A 103 (2) (2003) 387) we formulated a conditional chromatic number theorem, which described a setting in which the chromatic number of the plane takes on two different values depending upon the axioms for set theory. We also constructed an example of a distance graph on the real line R whose chromatic number depends upon the system of axioms we choo...
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملذخیره 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: Journal of the Australian Mathematical Society
سال: 2004
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700013574