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Acyclic and k-distance coloring of the grid
2003
Information Processing Letters
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¦ @ ¼ j 6 H Q P k q c x ¬ n B H A 2 ! ...
k @ Y S £ ¥ ¤ p i 1 q ¦ t v w » e v y W h k n k 0 £ 2 0 @ I t v w s e v y h 6 8 w x p r 6 I t 5 ( ® g ¥ t ¡ s t v p » " y 2 x p r t v y e 2 £ · r I t 5 ( v " ¥ t ® 1 ¤ q ' ¡ I t x ( 5 ( n £ ¢ s 9 % 2 ...
H v C S 9 g d 9 " A ¡ B 1 ' F " 7 % k r @ 9 p 9 g 7 3 I 1 Ỳ a U 3 I 9 " 9 g % ' I ) ...
doi:10.1016/s0020-0190(03)00232-1
fatcat:twbage3fqfbzthyx2butsz5g7u
Page 8408 of Mathematical Reviews Vol. , Issue 2000m
[page]
2000
Mathematical Reviews
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For a graph G of size m > 1 and an integer k with 1 <k < m, the k-jump graph J,(G) is that graph whose vertices corre- spond to the edge-induced subgraphs of size k of G and where two vertices of J,(G) ...
An acyclic coloring of a graph G is an assignment of colors to the vertices of G such that each vertex has exactly one color, each edge has exactly two colors, and each cycle has at least three colors. ...
Star coloring of graphs
2004
Journal of Graph Theory
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The star chromatic number of an undirected graph G, denoted by χs(G), is the smallest integer k for which G admits a star coloring with k colors. ...
In this paper, we give the exact value of the star chromatic number of different families of graphs such as trees, cycles, complete bipartite graphs, outerplanar graphs and 2-dimensional grids. ...
The authors wish to thank the anonymous referees for many valuable remarks that helped to improve this paper. ...
doi:10.1002/jgt.20029
fatcat:cx6yostynjhnxdfhoazracwxyu
On the Acyclic Chromatic Number of Hamming Graphs
2008
Graphs and Combinatorics
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The acyclic chromatic number of a graph G is the minimum number k such that G has an acyclic coloring with k colors. ...
In this paper, acyclic colorings of Hamming graphs, products of complete graphs, are considered. Upper and lower bounds on the acyclic chromatic number of Hamming graphs are given. ...
The authors thank the referee for useful comments. On the acyclic chromatic number of Hamming graphs ...
doi:10.1007/s00373-008-0798-4
fatcat:aoo5qggdy5fkxpbg7vel7p6224
Page 1712 of Mathematical Reviews Vol. , Issue 2004c
[page]
2004
Mathematical Reviews
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2004c:05069 05
2004c:05069 0S5CIS 68R10
Fertin, Guillaume (F-NANT-IR; Nantes) ;
Godard, Emmanuel (F-BORD-LB; Talence) ;
Raspaud, André (F-BORD-LB; Talence)
Acyclic and k-distance coloring of the grid. ...
the same color and (ii) for any two colors i and /, the subgraph induced by the vertices colored i or j is acyclic; and (2) k-distance coloring of graphs, in which every vertex must be colored in such ...
Nondeterminism versus determinism of finite automata over directed acyclic graphs
1994
Bulletin of the Belgian Mathematical Society Simon Stevin
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Three types of finite-state graph automata are compared over directed acyclic graphs (where vertices and edges are labelled). ...
We note the equivalence of these models, relate them to logical definability notions, and show that deterministic versions are strictly weaker (thus correcting an error of [9]). ...
Consider the graphs G k = (V k , E k , µ) where V k = {0, . . . , 2k − 1}, and E k consists of the edges {(2i, 2i + 1) | i < k} colored c 2 and {(2i, 2i − 1(mod(2k))) | 0 < i < k} colored c 1 . d d d © ...
doi:10.36045/bbms/1103408550
fatcat:b6vwobes35fitmxrikut4gj7q4
Symmetry Detection for Quadratic Optimization Using Binary Layered Graphs
2019
Processes
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This paper highlights the importance of detecting and classifying symmetry and shows that knowledge of this symmetry enables quick approximation of a highly symmetric optimization problem. ...
We enter the binary layered graphs into the software package nauty that generates important symmetric properties of the original problem. ...
Abbreviations The following abbreviations are used in this manuscript:
MINLP Mixed-integer nonlinear optimization QCQP Quadratically-constrained quadratic optimization ...
doi:10.3390/pr7110838
fatcat:s2uuuxa73vggjj3kn7d4w4t33q
Compact Grid Representation of Graphs
[chapter]
2012
Lecture Notes in Computer Science
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Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. ...
A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. ...
Similarly, for a directed graph G, δ − (v) denotes the in-degree of a vertex v and Δ − (G) the maximum vertex in-degree in G.Lemma 1.Let G be a connected, directed, acyclic and not isomorphic to K 5 graph ...
doi:10.1007/978-3-642-34191-5_16
fatcat:tpdtata7w5eerh4nyics6zzb7e
Dynamic monopolies and feedback vertex sets in hexagonal grids
2011
Computers and Mathematics with Applications
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and toroidal hexagonal grids. ...
We use this equivalence to provide exact values for the minimum size of dynamic monopolies of planar hexagonal grids, as well as upper and lower bounds on the minimum size of dynamic monopolies of cylindrical ...
The authors would like to thank the reviewers for their reports which led to significant improvements in this manuscript; the authors are grateful for the time and care that went into preparing these reports ...
doi:10.1016/j.camwa.2011.09.047
fatcat:3wn4cak3zrfqrcifjyqq2oe5b4
Acyclic coloring of graphs
1991
Random structures & algorithms (Print)
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The smallest number of colors required to acyclically vertex color a graph is called its acyclic chromatic number and is denoted by a(G). ...
Similarly, the smallest number of colors required to acyclically edge colors a graph is called its acyclic edge chromatic number and is denoted by a ′ (G). ...
Acyclic Vertex Coloring Fertin et al. [FGR03] have explored the acyclic vertex coloring of grids which are a subclass of the more general d-dimensional partial tori graphs. ...
doi:10.1002/rsa.3240020303
fatcat:dq3ainuygfcrnajo2si56jnada
Fast convergence in self-stabilizing wireless networks
2006
12th International Conference on Parallel and Distributed Systems - (ICPADS'06)
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Similarly, the height of the induced DAG is much lower than the linear dependency on the size of the color domain (that was previously announced). ...
The advent of large scale multi-hop wireless networks highlights problems of fault tolerance and scale in distributed systems, motivating designs that autonomously recover from transient faults and spontaneous ...
We have run Algorithm N1 for distance-1 and distance-2 colorings with these scheduling hypothesis and modes over a random geometric topology and a grid with a varying number of neighbors per node and different ...
doi:10.1109/icpads.2006.47
dblp:conf/icpads/MittonFLST06
fatcat:acdghqqvtneovg7w33npnu6wyq
Acyclic Coloring of Graphs of Maximum Degree $\Delta$
2005
Discrete Mathematics & Theoretical Computer Science
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The acyclic chromatic number of $G$ is the least number of colors necessary to acyclically color $G$, and is denoted by $a(G)$. ...
International audience An acyclic coloring of a graph $G$ is a coloring of its vertices such that: (i) no two neighbors in $G$ are assigned the same color and (ii) no bicolored cycle can exist in $G$. ...
We also note that there exist graphs of maximum degree 5 with acyclic chromatic number 6, such as the complete graph K 6 , the complete bipartite graph K 5,5 or the circulant graph C 8 (1, 2, 4) . ...
doi:10.46298/dmtcs.3450
fatcat:jldhrresqbc6fepwg5skyjs6rq
Eternal dominating sets on digraphs and orientations of graphs
[article]
2018
arXiv
pre-print
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We also study these two parameters on trees, cycles, complete graphs, complete bipartite graphs, trivially perfect graphs and different kinds of grids and products of graphs. ...
We study the eternal dominating number and the m-eternal dominating number on digraphs. We generalize known results on graphs to digraphs. ...
Let p be the color of v i and q be the color of u j . Then, we assign to w i,j the color r = p + q mod k. Let r ′ be a color different from r. ...
arXiv:1805.09623v1
fatcat:mgctg2j2uzci7pxwqf4juv444u
DAGView: An Approach for Visualizing Large Graphs
[chapter]
2013
Lecture Notes in Computer Science
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The aim of DAGView is to produce clear visualizations of directed acyclic graphs in which every edge and the potential existence of a path can be immediately spotted by the user. ...
The main algorithm is based on the layout of directed acyclic graphs but can be extended to handle directed graphs with cycles and undirected graphs, taking into account user preferences and/or constraints ...
Columns denote the origin-node of the edge, while the rows denote the target-node of the edge. If there is an edge (u, v) the cell at the intersection of column u and row v, is colored black. ...
doi:10.1007/978-3-642-36763-2_44
fatcat:jyxjxhcemzferos2xgep37lwga
Word-representability of subdivisions of triangular grid graphs
[article]
2015
arXiv
pre-print
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A subdivision of a triangular grid graph is replacing some of its cells by plane copies of the complete graph K_4. ...
A graph G=(V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if (x,y)∈ E. ...
Note that in our definition, a triangular grid graph does not have to be an induced subgraph of T ∞ . It is easy to see that T ∞ is 3-colorable, and thus any triangular grid graph is 3-colorable. ...
arXiv:1503.08002v1
fatcat:di3tjglesrazhmjdrgtpvecrpa
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