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### Coloring squares of graphs with mad constraints [article]

Hervé Hocquard and Seog-Jin Kim and Théo Pierron
2019 arXiv   pre-print
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  that roughly (2k − 1)∆ colors are sufficient to color the square of every graph G with mad(G) < 2k and ∆(G) = ∆.  ...

### Coloring squares of graphs with mad constraints

Hervé Hocquard, Seog-Jin Kim, Théo Pierron
2019 Discrete Applied Mathematics
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  that roughly (2k − 1)∆ colors are sufficient to color the square of every graph G with mad(G) < 2k and ∆(G) = ∆.  ...

### List coloring the square of sparse graphs with large degree [article]

Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou
2013 arXiv   pre-print
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  ...

### Sufficient sparseness conditions for G^2 to be (Δ+1)-choosable, when Δ>5 [article]

Daniel W. Cranston, Riste Škrekovski
2013 arXiv   pre-print
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.  ...

### Efficient incorporation of Markov Random Fields in change detection

H. Aances, A. A. Nielsen, J. M. Carstensen, R. Larsen, B. Ersboll
2009 2009 IEEE International Geoscience and Remote Sensing Symposium
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.  ...

### An Introduction to the Discharging Method via Graph Coloring [article]

Daniel W. Cranston, Douglas B. West
2016 arXiv   pre-print
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.  ...

### Temporal Subspace Clustering for Human Motion Segmentation

Sheng Li, Kang Li, Yun Fu
2015 2015 IEEE International Conference on Computer Vision (ICCV)
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-  ...

### An introduction to the discharging method via graph coloring

Daniel W. Cranston, Douglas B. West
2017 Discrete Mathematics
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.  ...

### Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable [article]

Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou
2013 arXiv   pre-print
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  ...

### The chromatic number of signed graphs with bounded maximum average degree [article]

Fabien Jacques, Alexandre Pinlou
2021 arXiv   pre-print
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.  ...

### Linear choosability of graphs

Louis Esperet, Mickaël Montassier, André Raspaud
2008 Discrete Mathematics
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  ).  ...

### Robust Radiometric Normalization of Multitemporal Satellite Images via Block Adjustment without Master Images

Kunbo Liu, Tao Ke, Pengjie Tao, Jianan He, Ke Xi, Kaijun Yang
2020 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
INTRODUCTION ADIOMETRIC normalization aims at reducing the radiation differences between images by adjusting the color of each image .  ...  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.  ...

### Randomized view planning and occlusion removal for mosaicing building facades

C. Rasmussen, T. Korah, W. Ulrich
2005 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems
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.  ...

### 2-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4 [article]

Hoang La, Kenny Štorgel
2022 arXiv   pre-print
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  1 presented the first results on injective colorings of planar graphs and later Acknowledgements Both authors were supported by the research grant PHC PROTEUS  ...

### Incidence coloring of graphs with high maximum average degree [article]

Marthe Bonamy, Hervé Hocquard, Samia Kerdjoudj, André Raspaud
2015 arXiv   pre-print
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  , the result of Theorem 7.1 is true for ∆ ≤ 3. More precisely every graph with ∆(G) ≤ 3, admits an incidence (∆(G) + 3, 3)-coloring.  ...
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