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Coloring squares of graphs with mad constraints
[article]
2019
arXiv
pre-print
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In this paper, we prove that the square of every graph G with mad(G)<4 and Δ(G) ≥ 8 is (3Δ(G)+1)-choosable and even correspondence-colorable. ...
A proper vertex k-coloring of a graph G=(V,E) is an assignment c:V→{1,2,...,k} of colors to the vertices of the graph such that no two adjacent vertices are associated with the same color. ...
Charpentier proved [4] that roughly (2k − 1)∆ colors are sufficient to color the square of every graph G with mad(G) < 2k and ∆(G) = ∆. ...
arXiv:1902.08135v1
fatcat:i6uxc7rbrjh5xiunhlla4u4ota
Coloring squares of graphs with mad constraints
2019
Discrete Applied Mathematics
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In this paper, we prove that the square of every graph G with mad(G) < 4 and ∆(G) 8 is (3∆(G) + 1)-choosable and even correspondence-colorable. ...
A proper vertex k-coloring of a graph G = (V, E) is an assignment c : V → {1, 2, . . . , k} of colors to the vertices of the graph such that no two adjacent vertices are associated with the same color. ...
Charpentier proved [5] that roughly (2k − 1)∆ colors are sufficient to color the square of every graph G with mad(G) < 2k and ∆(G) = ∆. ...
doi:10.1016/j.dam.2019.08.011
fatcat:jkt5rl4ynfccxhimeyxd4qtm3m
List coloring the square of sparse graphs with large degree
[article]
2013
arXiv
pre-print
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We strengthen their result and prove that there exists a function f such that the square of any graph with maximum average degree m<3 and maximum degree Δ≥ f(m) is list (Δ+1)-colorable. ...
Borodin et al. proved in 2004 and 2008 that the squares of planar graphs of girth at least seven and sufficiently large maximum degree Δ are list (Δ+1)-colorable, while the squares of some planar graphs ...
A k-coloring of the square of a graph G (also known as 2-distance k-coloring of G) is therefore a coloring of the vertices of G with k colors such that two vertices that are adjacent or have a common neighbor ...
arXiv:1308.4197v1
fatcat:rruvzpkgnfbvhnru7voqbpxmbe
Sufficient sparseness conditions for G^2 to be (Δ+1)-choosable, when Δ>5
[article]
2013
arXiv
pre-print
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We determine the list chromatic number of the square of a graph (G^2) in terms of its maximum degree Δ when its maximum average degree, denoted (G), is sufficiently small. ...
In particular, if G is planar with girth g> 7+12/Δ-2, then (G^2)=Δ+1. Under the same conditions, ^i(G)=Δ, where ^i is the list injective chromatic number. ...
Finally, we color the v i with 4 | (i + 2), each of which has an available color. Remove all 2-vertices of (C5), and by minimality color the square of the resulting graph. ...
arXiv:1303.5136v3
fatcat:rod65iobffhmreta4ozygabmc4
Efficient incorporation of Markov Random Fields in change detection
2009
2009 IEEE International Geoscience and Remote Sensing Symposium
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We do this by exploiting recent advances in graph based algorithms for Markov Random Fields. This is combined with an IR-MAD change detector, and demonstrated on real data with good results. ...
We here address the issue of efficient incorporation of local homogeneity constraints into change detection algorithms. ...
., for which the sum of squared, standardized MAD variates is small, and small weights being assigned to observations for which the sum is large. ...
doi:10.1109/igarss.2009.5417856
dblp:conf/igarss/AanaesNCLE09
fatcat:2tcrhasgujbrljzxb6zsu3iheq
An Introduction to the Discharging Method via Graph Coloring
[article]
2016
arXiv
pre-print
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Our aim is not to exhaustively survey results proved by this technique, but rather to demystify the technique and facilitate its wider use, using applications in graph coloring as examples. ...
We provide a "how-to" guide to the use and application of the Discharging Method. ...
All the constraints forcing vertices of G to have distinct colors are present also in G ′ , so any proper coloring of the square of G ′ can also be used on V (G ′ ) in G. ...
arXiv:1306.4434v2
fatcat:znrp36yihfcwfj2fcxy3hdaf6y
Temporal Subspace Clustering for Human Motion Segmentation
2015
2015 IEEE International Conference on Computer Vision (ICCV)
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After constructing an affinity graph using the codings, multiple temporal segments can be grouped via spectral clustering. ...
Experimental results on three action and gesture datasets demonstrate the effectiveness of our approach. ...
Acknowledgment This research is supported in part by the National Science Foundation (NSF) CNS award 1314484, Office of Naval Research (ONR) award N00014-12-1-1028, ONR Young Investigator Award N00014- ...
doi:10.1109/iccv.2015.506
dblp:conf/iccv/LiLF15
fatcat:fchcio5lfvgxxjahijjqtgmmby
An introduction to the discharging method via graph coloring
2017
Discrete Mathematics
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Our aim is not to exhaustively survey results proved by this technique, but rather to demystify the technique and facilitate its wider use, using applications in graph coloring as examples. ...
We provide a "how-to" guide to the use and application of the Discharging Method. ...
All the constraints forcing vertices of G to have distinct colors are present also in G ′ , so any proper coloring of the square of G ′ can also be used on V (G ′ ) in G. ...
doi:10.1016/j.disc.2016.11.022
fatcat:neapvvzudbd2th7wv5qj5kf4ea
Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable
[article]
2013
arXiv
pre-print
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For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. ...
More generally, we show that graphs with maximum average degree less than 3 and D>=17 are list 2-distance (D+2)-colorable. The proof can be transposed to list injective (D+1)-coloring. ...
This is equivalent to a proper vertex-coloring of the square of G, which is defined as a graph with the same set of vertices as G, where two vertices are adjacent if and only if they are adjacent or have ...
arXiv:1301.7090v1
fatcat:hnp4emirqvgzroy4ex5v5fuxjm
The chromatic number of signed graphs with bounded maximum average degree
[article]
2021
arXiv
pre-print
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The maximum average degree mad(G) of a graph G is the maximum of the average degrees of all the subgraphs of G. ...
A signed graph is a simple graph with two types of edges: positive and negative edges. Switching a vertex v of a signed graph corresponds to changing the type of each edge incident to v. ...
Square vertices can be of any degree. ...
arXiv:2104.11121v2
fatcat:xfg6qgttszbdnevk2iqp5deote
Linear choosability of graphs
2008
Discrete Mathematics
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A proper vertex coloring of a non-oriented graph G is linear if the graph induced by the vertices of any two color classes is a forest of paths. ...
In this paper, we investigate the linear choosability for some families of graphs: graphs with small maximum degree, with given maximum average degree, outerplanar and planar graphs. ...
The best known bound for the chromatic number of the square of a planar graph was obtained by Molloy and Salavatipour (see [10] ). ...
doi:10.1016/j.disc.2007.07.112
fatcat:eoqjzc3jlnay3b7d6ltrd7wkwa
Robust Radiometric Normalization of Multitemporal Satellite Images via Block Adjustment without Master Images
2020
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
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INTRODUCTION ADIOMETRIC normalization aims at reducing the radiation differences between images by adjusting the color of each image [1]. ...
Satellite images which form a block are often acquired at different time or even by different satellites, so their colors are different. ...
(a) original IR-MAD based IRRA (b) modified IR-MAD based IRRA (c) local graph of red box in (a) (d) local graph of red box in (b) Fig. 15. ...
doi:10.1109/jstars.2020.3028062
fatcat:5lbft3zx45hv7lza2lduxrx3j4
Randomized view planning and occlusion removal for mosaicing building facades
2005
2005 IEEE/RSJ International Conference on Intelligent Robots and Systems
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of the facade provides a critical cue to correctly complete the mosaic. ...
We present two key parts of an ongoing robotic, vision-based architectural modeling project. ...
ACKNOWLEDGMENTS This work was supported by a grant from the University of Delaware Research Foundation. ...
doi:10.1109/iros.2005.1545484
dblp:conf/iros/RasmussenKU05
fatcat:5s2k23gwine47jxdwq25flrmby
2-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4
[article]
2022
arXiv
pre-print
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Additionally, we prove that planar graphs with Δ = 4 are injectively list (Δ + 7)-colorable and exact square list (Δ + 6)-colorable. ...
In the past various distance based colorings on planar graphs were introduced. We turn our focus to three of them, namely 2-distance coloring, injective coloring, and exact square coloring. ...
In 2005, Doyon, Hahn, and Raspaud [19] 1 presented the first results on injective colorings of planar graphs and later
Acknowledgements Both authors were supported by the research grant PHC PROTEUS ...
arXiv:2205.07968v1
fatcat:ppnmd5noprdcxpo5jgkj7ola6i
Incidence coloring of graphs with high maximum average degree
[article]
2015
arXiv
pre-print
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An incidence of an undirected graph G is a pair (v,e) where v is a vertex of G and e an edge of G incident with v. ...
In 2005, Hosseini Dolama et al. ds05 proved that every graph with maximum average degree strictly less than 3 can be incidence colored with Δ+3 colors. Recently, Bonamy et al. ...
By using Theorem 1 or the result of [8] , the result of Theorem 7.1 is true for ∆ ≤ 3. More precisely every graph with ∆(G) ≤ 3, admits an incidence (∆(G) + 3, 3)-coloring. ...
arXiv:1412.6803v2
fatcat:alckuuprjvblxhmihv4ybzlhq4
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