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A Turing Test for artificial nets devoted to vision. [PDF]
Vila-Tomás J +4 more
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Situational motionless camouflage of a loliginid squid. [PDF]
Nakajima R +8 more
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The adaptable chromatic number and the chromatic number
J. Graph Theory, 2017Consider a graph \(G\) whose edges are colored (perhaps not properly) using the colors \(1, \ldots, k\). A \(k\)-adapted coloring of \(G\), relative to the given edge coloring, is an assignment of the colors \(1, \ldots, k\) to the vertices of \(G\) (not necessarily a proper coloring) such that no edge shares its color with both of its endpoints. Thus,
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ON THE CHROMATIC NUMBERS OF FUNCTIGRAPHS
Journal of Interconnection Networks, 2012The chromatic number of a graph G, denoted χ(G) is the minimum number of colors needed to color vertices of G so that no two adjacent vertices share the same color. A functigraph over a given graph is obtained as follows: Let G' be a disjoint copy of a given G and f be a function f : V(G) → V(G').
George Qi, Shenghao Wang, Weizhen Gu
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On the Strong Chromatic Number
Combinatorics, Probability and Computing, 2004The author proves that for every finite graph \(G\) the strong chromatic number of \(G\) is at most \(3\Delta(G)-1\), where \(\Delta(G)\) is the maximum vertex degree of \(G\).
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Chromatic Scheduling and the Chromatic Number Problem
Management Science, 1972The chromatic scheduling problem may be defined as any problem in which the solution is a partition of a set of objects. Since the partitions may not be distinct, redundant solutions can be generated when partial enumeration techniques are applied to chromatic scheduling problems. The necessary theory is developed to prevent redundant solutions in the
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On the Chromatic Number of Graphs
Journal of Optimization Theory and Applications, 2001Computing the chromatic number of a graph is NP-hard---in fact, it is NP-hard to colour a graph with fewer than twice the minimum number of colours [\textit{M. R. Garey} and \textit{D. S. Johnson}, The complexity of near-optimal graph coloring, J. Assoc. Comput. Mach. 23, 43-49 (1976; Zbl 0322.05111)].
FESTA, PAOLA, S. BUTENKO, P. M. PARDALOS
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Graphs Whose Circular Chromatic Number Equals the Chromatic Number
Combinatorica, 1999The circular chromatic number of a graph is the infimum (in fact, the minimum) of \({k}/{d}\) where there is a coloring \(f\) of the vertices with colors \(1,2,\dots,k\) in such a way that \(d\leq | f(x)-f(y)| \leq k-d\) holds when \(x\), \(y\) are adjacent.
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