Filters








30,698 Hits in 4.3 sec

Vector Coloring the Categorical Product of Graphs [article]

Chris Godsil, David E. Roberson, Brendan Rooney, Robert Šámal, Antonios Varvitsiotis
2018 arXiv   pre-print
,p_n of a graph G, the assignment (i,ℓ) p_i is a vector t-coloring of the categorical product G × H.  ...  Furthermore, we prove a necessary and sufficient condition for when all of the optimal vector colorings of the product can be expressed in terms of the optimal vector colorings of the factors.  ...  Our primary focus in this work is on vector colorings of categorical products of graphs.  ... 
arXiv:1801.08243v1 fatcat:6ok7wpocgbcuharybxbtzef2iq

Hedetniemi's conjecture for Kneser hypergraphs [article]

Hossein Hajiabolhassan, Frédéric Meunier
2014 arXiv   pre-print
One of the most famous conjecture in graph theory is Hedetniemi's conjecture stating that the chromatic number of the categorical product of graphs is the minimum of their chromatic numbers.  ...  Using a suitable extension of the definition of the categorical product, Zhu proposed in 1992 a similar conjecture for hypergraphs.  ...  The research of Hossein Hajiabolhassan is supported by ERC advanced grant GRACOL. Part of this work was done during a visit of Hossein Hajiabolhassan to the Université Paris Est.  ... 
arXiv:1410.3021v1 fatcat:dryncow77zh7bkrzqlxaxycxza

Sabidussi Versus Hedetniemi for Three Variations of the Chromatic Number [article]

Chris Godsil, David Roberson, Robert Šámal, Simone Severini
2013 arXiv   pre-print
We also prove an analog of Hedetniemi's conjecture for Lovasz theta of the complement, i.e. that its value on the categorical product of graphs is equal to the minimum of its values on the factors.  ...  We investigate vector chromatic number, Lovasz theta of the complement, and quantum chromatic number from the perspective of graph homomorphisms.  ...  An equally, if not more, well known conjecture of Hedetniemi proposes that the chromatic number of the categorical product of two graphs is equal to the minimum of the chromatic numbers of the factors.  ... 
arXiv:1305.5545v1 fatcat:vmi3gke4ijg5bfxqqttknsfm7i

Sabidussi versus Hedetniemi for three variations of the chromatic number

Chris Godsil, David E. Roberson, Robert Šámal, Simone Severini
2015 Combinatorica  
We also prove an analog of Hedetniemi's conjecture forθ, i.e. that its value on the categorical product of graphs is equal to the minimum of its values on the factors.  ...  We prove an analog of Sabidussi's theorem for each of these parameters, i.e. that for each of the parameters, the value on the Cartesian product of graphs is equal to the maximum of the values on the factors  ...  An equally, if not more, well known conjecture of Hedetniemi proposes that the chromatic number of the categorical product of two graphs is equal to the minimum of the chromatic numbers of the factors.  ... 
doi:10.1007/s00493-014-3132-1 fatcat:darrtl6kivflfbxkdtzf4544ay

Dynamics on networks I. Combinatorial categories of modular continuous-time systems [article]

R. E. Lee DeVille, Eugene Lerman
2011 arXiv   pre-print
This makes precise the relation between dynamical systems living on networks and the combinatorial structure of the underlying directed graphs, allowing us to exploit the relation in new and interesting  ...  Each such model, as a category, is a fibration over an appropriate category of labeled directed graphs.  ...  We thank Charles Rezk, Bertrand Guillou, and Matthew Ando for a number of useful conversations.  ... 
arXiv:1008.5359v2 fatcat:hkxvc776g5h5ji6mtqm2rjlmje

Universal Completability, Least Eigenvalue Frameworks, and Vector Colorings

Chris Godsil, David E. Roberson, Brendan Rooney, Robert Šámal, Antonios Varvitsiotis
2017 Discrete & Computational Geometry  
In the second part of this work we study uniquely vector colorable (UVC) graphs, i.e., graphs for which the semidefinite program corresponding to the Lovász theta number (of the complementary graph) admits  ...  Lastly, we show that least eigenvalue frameworks of 1-walk-regular graphs always provide optimal vector colorings and furthermore, we are able to characterize all optimal vector colorings of such graphs  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1007/s00454-017-9899-2 pmid:32025074 pmcid:PMC6979529 fatcat:e7aaymdhbnefvlqzduiv4flfie

Chromatic Learning for Sparse Datasets [article]

Vladimir Feinberg, Peter Bailis
2020 arXiv   pre-print
This approach, which we call Chromatic Learning (CL), obtains a low-dimensional dense feature representation by performing graph coloring over the co-occurrence graph of features---an approach previously  ...  CL exhibits linear parallelizability and consumes memory linear in the size of the co-occurrence graph.  ...  Acknowledgments and Disclosure of Funding The authors would like to thank Jon Gjengset, Greg Valiant, Barak Oshri, Arnaud Autef, and Kai Sheng Tai for helpful comments.  ... 
arXiv:2006.03779v1 fatcat:77525vjox5bghbfdrccsysdzgi

A worthy family of semisymmetric graphs

Steve Wilson
2003 Discrete Mathematics  
We display a family of bi-transitive graphs DN (a; b) which can be used for this purpose and we show that their products are semisymmetric by applying vectors due to Ivanov.  ...  In this paper, we construct semisymmetric graphs in which no two vertices have exactly the same neighbors.  ...  One possible product of the two graphs (called the categorical product and other names; see [9, 12, 17, 19] ) of these two is the graph whose vertices are ordered pairs of vertices from 1 and 2 , two  ... 
doi:10.1016/s0012-365x(03)00048-7 fatcat:zzdf4b33nzcrniyp3niwrmd6oe

Correspondence Propagation with Weak Priors

H. Wang, S. Yan, J. Liu, X. Tang, T.S. Huang
2009 IEEE Transactions on Image Processing  
; then the geometric neighborhood of the pairwise assignment is represented by a categorical product graph, along which the reliable correspondences are propagated; and finally a closed-form solution for  ...  Extensive experiments on both toy examples and real-world applications demonstrate the superiority of our algorithm over the state-of-the-art feature matching techniques.  ...  corresponding graph is the categorical product graph of and .  ... 
doi:10.1109/tip.2008.2006602 pmid:19095525 fatcat:aunyusntzrffdcmu6hwlleqpdy

Image categorization by learning with context and consistency

Zhiwu Lu, Horace H.S. Ip
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
matrix of a graph.  ...  To the best of our knowledge, this is the first application of kernel methods and 2D Markov models simultaneously to image categorization.  ...  Acknowledgements The work described in this paper was supported by a grant from the Research Council of Hong Kong SAR, China (Project No.  ... 
doi:10.1109/cvpr.2009.5206851 dblp:conf/cvpr/LuI09a fatcat:f223rgnavnerportvhrd6qaxqu

Image categorization by learning with context and consistency

Zhiwu Lu, H.H.S. Ip
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
matrix of a graph.  ...  To the best of our knowledge, this is the first application of kernel methods and 2D Markov models simultaneously to image categorization.  ...  Acknowledgements The work described in this paper was supported by a grant from the Research Council of Hong Kong SAR, China (Project No.  ... 
doi:10.1109/cvprw.2009.5206851 fatcat:vc75h3mph5dzrkeezjekmubexm

Automated Guava Classification Technique using Artificial Neural Network and Artificial Ant ColonyRaed Qaqish ORCID: 0000-0003-2317-6183

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
Guava is one of the main agricultural products in the northern part of Jordan. The classification of fruit products is an essential part in the packaging, shipment, and marketing processes.  ...  The proposed research will provide a rich analysis and investigation of several features of the problem at hand. Our study will convey and integrate shape, color, and texture descriptors.  ...  After extracting the histogram vectors, the first element of the vector, black color, has been converted into zero. In this way, the black color has been deleted.  ... 
doi:10.35940/ijitee.i7901.078919 fatcat:52llor4liretncalre42fau3bq

Sentiment Analyzing by Dictionary based Approach

Fatehjeet Kaur, Rekha Bhatia
2016 International Journal of Computer Applications  
Sentiment analysis has emerged as a field of study since the widespread of World Wide Web and internet.  ...  Opinion refers to withdrawal of lines or phrase in the unprocessed and immense data which express an opinion. Sentiment analysis further recognizes the polarity of the viewpoint being extricated.  ...  All these classifiers have almost similar accuracy for new attribute vector. The new attribute(feature) vector functions well for electronic products domain.  ... 
doi:10.5120/ijca2016911814 fatcat:c3ozdmtnwnfibhti4whhsznnom

Hedetniemi's Conjecture Via Altermatic Number [article]

Meysam Alishahi, Hossein Hajiabolhassan
2016 arXiv   pre-print
--University of Michigan, 1966] asserts that the chromatic number of the categorical product of two graphs G and H is {χ(G),χ(H)}.  ...  Also, we present a tight lower bound for the chromatic number of the categorical product of two graphs in term of their altermatic and strong altermatic numbers.  ...  A part of this paper was written while Hossein Hajiabolhassan was visiting School of Mathematics, Institute for Research in Fundamental Sciences (IPM). He acknowledges the support of IPM.  ... 
arXiv:1403.4404v5 fatcat:3f5b5v4hpzewzdqmtffxkdmotm

Coloring Properties of Categorical Product of General Kneser Hypergraphs [article]

Roya Abyazi Sani, Meysam Alishahi, Ali Taherkhani
2017 arXiv   pre-print
More than 50 years ago Hedetniemi conjectured that the chromatic number of categorical product of two graphs is equal to the minimum of their chromatic numbers.  ...  In this paper, we shall present some colorful type results for the coloring of categorical product of general Kneser hypergraphs, which generalize the Hajiabolhassan-Meunier result.  ...  Introduction and Main Results For two graphs G and H, their categorical product G × H is the graph defined on the vertex set V (G) × V (H) such that two vertices (g, h) and (g ′ , h ′ ) are adjacent whenever  ... 
arXiv:1705.00223v1 fatcat:g7fs55hg75avfoujwi3zkmb3am
« Previous Showing results 1 — 15 out of 30,698 results