منابع مشابه
Coloring Some Finite Sets In
This note relates to bounds on the chromatic number χ(R) of the Euclidean space, which is the minimum number of colors needed to color all the points in R so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn in R n was introduced showing that χ(R) ≥ χ(Gn) ≥ (1 + o(1)) n 2 6 . For many years, this bound has been remaining the best known bound for the ...
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We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function in noncommuting variables for which we give a deletion-contraction formula. In the case of graphs this symmetric function in noncommuting variab...
متن کاملHitting Sets Online and Unique-Max Coloring
We consider the problem of hitting sets online. The hypergraph (i.e., rangespace consisting of points and ranges) is known in advance, and the ranges to be stabbed are input one-by-one in an online fashion. The online algorithm must stab each range upon arrival. An online algorithm may add points to the hitting set but may not remove already chosen points. The goal is to use the smallest number...
متن کاملRestricted coloring problems
In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of P4-tidy graphs and (q, q − 4)-graphs, for every fixed q. These classes include cographs, P4-sparse and P4-lite graphs. We also obtain a polynomial time algorithm to determine the Grundy number of (q, q − 4)-graphs. All these coloring pro...
متن کاملColoring finite subsets of uncountable sets
It is consistent for every 1 ≤ n < ω that 2 = ωn and there is a function F : [ωn] <ω → ω such that every finite set can be written at most 2 − 1 ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least 1 2 ∑n i=1 ( n+i n )( n i ) ways as the union of two sets with the same color. 0 Introduction In [6] we proved ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12559-9