Computing the list chromatic index of graphs

2018 ◽  
Vol 52-53 ◽  
pp. 182-191
Author(s):  
Uwe Schauz
Keyword(s):  
1994 ◽  
Vol 124 (1-3) ◽  
pp. 173-177
Author(s):  
E. Sampathkumar ◽  
G.D. Kamath
Keyword(s):  

2017 ◽  
Vol 609 ◽  
pp. A12 ◽  
Author(s):  
M. Zechmeister ◽  
A. Reiners ◽  
P. J. Amado ◽  
M. Azzaro ◽  
F. F. Bauer ◽  
...  

Context. The CARMENES survey is a high-precision radial velocity (RV) programme that aims to detect Earth-like planets orbiting low-mass stars. Aims. We develop least-squares fitting algorithms to derive the RVs and additional spectral diagnostics implemented in the SpEctrum Radial Velocity AnaLyser (SERVAL), a publicly available python code. Methods. We measured the RVs using high signal-to-noise templates created by coadding all available spectra of each star. We define the chromatic index as the RV gradient as a function of wavelength with the RVs measured in the echelle orders. Additionally, we computed the differential line width by correlating the fit residuals with the second derivative of the template to track variations in the stellar line width. Results. Using HARPS data, our SERVAL code achieves a RV precision at the level of 1 m/s. Applying the chromatic index to CARMENES data of the active star YZ CMi, we identify apparent RV variations induced by stellar activity. The differential line width is found to be an alternative indicator to the commonly used full width half maximum. Conclusions. We find that at the red optical wavelengths (700–900 nm) obtained by the visual channel of CARMENES, the chromatic index is an excellent tool to investigate stellar active regions and to identify and perhaps even correct for activity-induced RV variations.


2017 ◽  
Vol 340 (5) ◽  
pp. 1143-1149 ◽  
Author(s):  
Mingfang Huang ◽  
Gexin Yu ◽  
Xiangqian Zhou

1987 ◽  
Vol 11 (3) ◽  
pp. 267-272 ◽  
Author(s):  
A. J. W. Hilton ◽  
Bill Jackson
Keyword(s):  

2008 ◽  
Vol 57 (4) ◽  
pp. 313-332 ◽  
Author(s):  
Pascal Ochem ◽  
Alexandre Pinlou ◽  
Éric Sopena

2017 ◽  
Vol 61 ◽  
pp. 835-839
Author(s):  
Borut Lužar ◽  
Martina Mockovčiaková ◽  
Roman Soták

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Olivier Togni

Graphs and Algorithms International audience The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching. In this paper, we present bounds for strong chromatic index of three different products of graphs in term of the strong chromatic index of each factor. For the cartesian product of paths, cycles or complete graphs, we derive sharper results. In particular, strong chromatic indices of d-dimensional grids and of some toroidal grids are given along with approximate results on the strong chromatic index of generalized hypercubes.


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