منابع مشابه
Colorings, Crossings, and Cliques
For r = 7, 8 we prove that if χ(G) = r, then cr(G) ≥ cr(Kr). The case r = 5 of the Weak Hajós Conjecture is equivalent to the Four Color Theorem, and the case r = 6 follows from a theorem of Oporowski and Zhao. We present partial results when r = 9.
متن کاملCrossings, Colorings, and Cliques
Albertson conjectured that if graph G has chromatic number r, then the crossing number of G is at least that of the complete graph Kr. This conjecture in the case r = 5 is equivalent to the four color theorem. It was verified for r = 6 by Oporowski and Zhao. In this paper, we prove the conjecture for 7 ≤ r ≤ 12 using results of Dirac; Gallai; and Kostochka and Stiebitz that give lower bounds on...
متن کاملBorder Crossings
It is well established by now that computer science has a number of concerns in common with natural language understanding. Common themes show up in particular with algorithmic aspects of text processing. This chapter gives an overview of border crossings from NLP to CS and back. Starting out from syntactic analysis, we trace our route via a philosophical puzzle about meaning, Hoare correctness...
متن کاملZero Crossings
In this essay, we presuppose basic knowledge of stochastic processes [1]. Let {Xt : t ≥ 0} be a zero mean, unit variance, stationary Gaussian process with twice differentiable correlation function r(|s − t|) = Cov(Xs,Xt). We wish to study the distribution of lengths of intervals between zeroes of Xt. There are two cases: the first in which r(τ) is analytic (implying differentiability up to all ...
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ژورنال
عنوان ژورنال: Medicine Anthropology Theory
سال: 2015
ISSN: 2405-691X
DOI: 10.17157/mat.2.1.214