منابع مشابه
Another six-coloring of the plane
A six-coloring of the Euclidean plane is constructed such that the distance 1 is not realized by any color except one, which does not realize the distance x/2 1. A 44-year-old problem due to Edward Nelson asks to find the chromatic number x(E 2) of the plane, i.e. the minimal number of colors that are required for coloring the plane so that no two points, a unit distance apart, lie on the same ...
متن کاملFour-coloring Six-regular Graphs on the Torus
A classic 3-color theorem attributed to Heawood [10, 11] (also observed by Kempe [16]) states that every even triangulation of the plane is 3-chromatic; by even we mean that every vertex has even degree. We are interested in the extent to which an analogous theorem carries over to even triangulations of the torus and to other surfaces of larger genus. In general, even triangulations of the toru...
متن کاملColoring squares of planar graphs with girth six
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture is known to be true for g ≥ 7 but false for g ∈ {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth at least six and sufficiently large max...
متن کاملRing chromosome instability evaluation in six patients with autosomal rings.
Ring chromosomes are often associated with abnormal phenotypes due to loss of genomic material and also because of ring instability at mitosis after sister chromatid exchange events. We investigated ring chromosome instability in six patients with ring chromosomes 4, 14, 15, and 18 by examining 48- and 72-h lymphocyte cultures at the first, second and subsequent cell divisions after bromodeoxyu...
متن کاملHighly enantioselective hydroamination to six-membered rings by heterobimetallic catalysts.
New bimetallic Zn/Zr salen-type systems were employed as catalysts in the asymmetric intramolecular hydroamination reaction. High enantioselectivity for the formation of piperidines of up to 98% ee were observed.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1948
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1948-0026312-5