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A Brooks-like result for graph powers [article]

Théo Pierron
2019 arXiv   pre-print
For k≥ 2, a similar result holds: excepted for Moore graphs, the naive upper bound can be lowered by 2.  ...  We investigate the chromatic number of powers of graphs, i.e. the graphs obtained from a graph G by adding an edge between every pair of vertices at distance at most k.  ...  From that perspective, Theorem 7 can be seen as a generalization of Brooks' theorem for powers of graphs.  ... 
arXiv:1912.11181v1 fatcat:ajfvb7p6ybh45ae4yjlfap4ogq

Book Review: Graph theory with applications

Blanche Descartes
1977 Bulletin of the American Mathematical Society  
The proof does indeed exhibit a graph in its last paragraph, but it is a piece of algebra for all of that.  ...  Does he want to prove that one Hamiltonian circuit implies at least 3 in a trivalent graph? He does it by a piece of algebra. Does he want a condition for a graph to have a perfect matching?  ... 
doi:10.1090/s0002-9904-1977-14245-6 fatcat:3ul5jnx6hfacfgreijgjk4a44q

Paul Catlin 1948–1995

Arthur M. Hobbs, Hong-Jian Lai, Neil Robertson
2001 Discrete Mathematics  
The main reduction method in [C26] is very powerful. With it, Catlin proved several signiÿcant results. We list a few below.  ...  Seldom does the originator of an idea see all of the possible uses of that idea, and the more powerful the idea, the less likely it is that the ÿrst paper will say all that can usefully be said.  ... 
doi:10.1016/s0012-365x(00)00065-0 fatcat:ubsvt26bxfhq3nvdobmhgzldoe

Graph theoretical analysis of resting-state MEG data: Identifying interhemispheric connectivity and the default mode

Joseph A. Maldjian, Elizabeth M. Davenport, Christopher T. Whitlow
2014 NeuroImage  
Graph theoretic voxelwise source space correlation connectivity analysis was performed for leakage-corrected and uncorrected data.  ...  Recent seed-based MEG analyses have shown interhemispheric connectivity using power envelope correlations.  ...  Special thanks to the Childress Institute for Pediatric Trauma at Wake Forest Baptist Medical Center for providing support to us and our collaborators, Joel Stitzel and Alex Powers, on the pediatric football  ... 
doi:10.1016/j.neuroimage.2014.03.065 pmid:24699016 pmcid:PMC4049007 fatcat:lzpglncxwzfzxmhzglesmr4njm

Page 434 of American Society of Civil Engineers. Collected Journals Vol. 120, Issue 4 [page]

1994 American Society of Civil Engineers. Collected Journals  
The next stage is to show the user a graph of the likely result of the test based on the initial soil description. This is where the knowledge-based system part comes into play.  ...  The graph drawing routine has been simplified from a general graphing routine available as a Power User tool from a standard HyperCard application stack.  ... 

Brooks' theorem on powers of graphs [article]

Marthe Bonamy, Nicolas Bousquet
2013 arXiv   pre-print
We prove that for k≥ 3, the bound given by Brooks' theorem on the chromatic number of k-th powers of graphs of maximum degree Δ≥ 3 can be lowered by 1, even in the case of online list coloring.  ...  Acknowledgements The authors would like to thank Daniel Cranston for suggesting the generalization to paintability.  ...  Jointly with the assumption that ∆ ≥ 3, this means for example that none of the graphs we consider is a cycle. We recall the following seminal Brooks-like theorem on choosability. Theorem 1.  ... 
arXiv:1310.5493v1 fatcat:m5vs4w6ezrhsrospx6qgm3rmdu

Exponential Capillary Pressure Functions in Sedimentary Rocks

Armin Afrough, Mehdi Bahari Moghaddam, Laura Romero-Zerón, Bruce J. Balcom, B. Nicot
2019 E3S Web of Conferences  
The Brooks-Corey power-law capillary pressure model is commonly imposed on core analysis data without verifying the validity of its underlying assumptions.  ...  We demonstrate that exponential models work much better for capillary pressure compared to the Brooks-Corey model over a wide saturation range.  ...  (a) is the relationship in a semi-log graph and (b) is the same data in the log-log form.  ... 
doi:10.1051/e3sconf/20198902005 fatcat:wji2gu44mffknmhlcoe4u7yfdq

Sensor Network Self-Organization Using Random Graphs

Richard R. Brooks
2009 International Journal of Distributed Sensor Networks  
This chapter discusses random network formalisms for designing, modeling, and analyzing survivable sensor networks. Techniques are given for determining critical values.  ...  They were specifically interested in clustered graphs, where edges are more likely to exist between nodes with common neighbors.  ...  Also, a known result from the percolation theory is that the inflection point for grid networks of Figure 3 shows the number of cloned keys detected for different settings and different numbers of clones  ... 
doi:10.1080/15501320802498307 fatcat:io4pvsiqxnhnracmx5pw6tfnf4

One-Chip Solution to Intelligent Robot Control: Implementing Hexapod Subsumption Architecture Using a Contemporary Microprocessor

Nikita Pashenkov, Ryuichi Iwamasa
2004 International Journal of Advanced Robotic Systems  
Next, we summarize original ideas on subsumption architecture implementation for a six-legged robot, as presented by its inventor Rodney Brooks in 1980's.  ...  We argue that this processor offers a unique set of hardware and software features, making it a practical development platform for robotics in general and for subsumption-based control architectures in  ...  The result, according to Brooks, is a development framework for robotics that offers a large number of advantages concerning robustness, buildability, and testability over the approaches emplyed in traditional  ... 
doi:10.5772/5625 fatcat:y2xu346jdretdbkb3uxmygnk4y

Brook Auto: High-Level Certification-Friendly Programming for GPU-powered Automotive Systems

Matina Maria Trompouki, Leonidas Kosmidis
2018 2018 55th ACM/ESDA/IEEE Design Automation Conference (DAC)  
In this paper we present Brook Auto, a high-level programming language for automotive GPU systems which removes these limitations.  ...  GPU-powered platforms are promising candidates for such computational tasks, however current low-level programming models challenge the accelerator software certification process, while they limit the  ...  , until it reached a plateau at 6.5× for larger graphs.  ... 
doi:10.1109/dac.2018.8465869 fatcat:hirnwummhzatxfcn3jovp72oey

Fast Distributed Algorithms for Brooks-Vizing Colourings (Extended Abstract)

David A. Grable, Alessandro Panconesi
1997 BRICS Report Series  
In this paper<br />we are concerned with the "distributed" version of a question stated by Vizing, concerning a Brooks-like theorem for sparse graphs.  ...  In 1948 Brooks gave a theorem<br />that characterizes the graphs which are not {colourable: a graph is<br />{colourable if and only if it is neither an odd cycle nor a + 1 clique (see, for instance, [2  ...  Acknowledgement Thanks to Micha l Karoński, Tomasz Luczak and Andrzej Ruciński for comments helpful to the presentation of this result.  ... 
doi:10.7146/brics.v4i37.18963 fatcat:csqnc6ujgrhyxc7a7yuyfvhr7y

Spatial and Temporal Heterogeneity Explain Disease Dynamics in a Spatially Explicit Network Model

Christopher P. Brooks, Janis Antonovics, Timothy H. Keitt
2008 American Naturalist  
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.  ...  Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen.  ...  Acknowledgments We would like to thank the many people who helped with the fieldwork, including H. Alexander, A. Davelos, M. Heuhsen, M. Hood, A. Jarosz, D. Stratton, S. Taliaferro, D. Taylor, and P.  ... 
doi:10.1086/589451 pmid:18662121 fatcat:asitwvxc4vayvoryf56y6fkw24

Optimal Layout of Multicast Groups Using Network Embedded Multicast Security in Ad Hoc Sensor Networks

R. R. Brooks, Brijesh Pillai, Michele C. Weigle, Matthew Pirretti
2007 International Journal of Distributed Sensor Networks  
When data is shared within regions, approaches using multicast communication require fewer encryptions for secure message exchange, resulting in a net power savings.  ...  We assume the initial point for h = 1. Table 1 shows the results for a network of 100 nodes with a communication range of 0.2.  ... 
doi:10.1080/15501320601062080 fatcat:6227q32s2behzh4iimxrzctt7e

Shape from shading using graph cuts

Ju Yong Chang, Kyoung Mu Lee, Sang Uk Lee
2008 Pattern Recognition  
In this paper, we investigate the applicability of graph cuts to the SFS (shape-from-shading) problem. We propose a new semi-global method for SFS using graph cuts.  ...  A new combinatorial optimization technique, the graph cuts method, is used for the minimization of the proposed energy functional.  ...  Acknowledgments This work was supported in part by the ITRC program by Ministry of Information and Communication and in part by Defense Acquisition Program Administration and Agency for Defense Development  ... 
doi:10.1016/j.patcog.2008.05.020 fatcat:p7hf3pys4jclnlwzsuivyiiggm

Page 3974 of Mathematical Reviews Vol. , Issue 84j [page]

1984 Mathematical Reviews  
The author bounds Var( X,) and uses it to give improved results for the Turan number. J. Spencer (Stony Brook, N.Y.) Karonski, Michat(PL-POZN) 84j:05094 On the number of k-trees in a random graph.  ...  Spectral moments are computed for these graphs up to eighth power. Comparability conditions of Muirhead are used to order the partial sums resulting from spectral moment codes.  ... 
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