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K-outerplanar Graph
In graph theory, a ''k''-outerplanar graph is a planar graph that has a planar embedding in which the vertices belong to at most k concentric layers. The outerplanarity index of a planar graph is the minimum value of k for which it is k-outerplanar. Definition An outerplanar graph In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two f ... (or 1-outerplanar graph) has all of its vertices on the unbounded (outside) face of the graph. A 2-outerplanar graph is a planar graph with the property that, when the vertices on the unbounded face are removed, the remaining vertices all lie on the newly formed unbounded face. And so on. More formally, a graph is k-outerplanar if it has a planar embedding such that, for every vertex, there is an alternating sequence of at most k faces and k vertices of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Dodecahedral Graph Layers
Rhombic may refer to: *Rhombus, a quadrilateral whose four sides all have the same length (often called a diamond) *Rhombic antenna, a broadband directional antenna most commonly used on shortwave frequencies * polyhedra formed from rhombuses, such as the rhombic dodecahedron or the rhombic triacontahedron or the rhombic dodecahedral honeycomb or the rhombic icosahedron or the rhombic hexecontahedron or the rhombic enneacontahedron or the trapezo-rhombic dodecahedron * other things that exhibit the shape of a rhombus, such as rhombic tiling, Rhombic Chess, rhombic drive, Rhombic Skaapsteker, rhombic egg eater, rhombic night adder, forest rhombic night adder {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with addit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outerplanar Graph
In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors and , or by their Colin de Verdière graph invariants. They have Hamiltonian cycles if and only if they are biconnected, in which case the outer face forms the unique Hamiltonian cycle. Every outerplanar graph is 3-colorable, and has degeneracy and treewidth at most 2. The outerplanar graphs are a subset of the planar graphs, the subgraphs of series–parallel graphs, and the circle graphs. The maximal outerplanar graphs, those to which no more edges can be added while preserving outerplanarity, are also chordal graphs and visibility graphs. History Outerplanar graphs were first studied and named by , in connection with the problem of determining the planarity of graphs formed by using a perfect matching to connec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treewidth
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests A forest is an ecosystem characterized by a dense community of trees. Hundreds of definitions of forest are used throughout the world, incorporating factors such as tree density, tree height, land use, legal standing, and ecological functio .... An example of graphs with treewidth at most 2 are the series–parallel graphs. The maximal graphs with treewidth exactly are called '' -trees'', and the graphs with treewidth at most are called '' partial -trees''. Many other well-studied graph families also have bounded treewidth. Treewidth may be formally defined in several equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal completi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science (journal)
''Theoretical Computer Science'' (''TCS'') is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science. The journal publishes 52 issues a year. It is abstracted and indexed by Scopus and the Science Citation Index. According to the Journal Citation Reports, its 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... is 0.827. References Computer science journals Elsevier academic journals Academic journals established in 1975 {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nested Triangles Graph
''Nested'' is the seventh studio album by Bronx-born singer, songwriter, and pianist Laura Nyro. It was released in 1978 on Columbia Records. Following on from her extensive tour to promote 1976's ''Smile'', which resulted in the 1977 live album '' Season of Lights'', Nyro retreated to her new home in Danbury, Connecticut, where she lived after spending her time in the spotlight in New York City. Nyro had a studio built at her home and recorded there the songs that comprised ''Nested''. The songs deal with themes such as motherhood and womanhood, and Nyro is notably more relaxed in her singing on the album. The instrumentation is laid back and smooth, similar to that of ''Smile'', but perhaps less jazz-inspired and more melodic. Nyro was assisted in production by Roscoe Harring, while Dale and Pop Ashby were chief engineers. Critics praised the album as a melodic return to form, and Nyro supported the album with a solo tour when she was heavily pregnant with her son Gil, who wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baker's Technique
In theoretical computer science, Baker's technique is a method for designing polynomial-time approximation schemes (PTASs) for problems on planar graphs. It is named after Brenda Baker, who announced it in a 1983 conference and published it in the ''Journal of the ACM'' in 1994. The idea for Baker's technique is to break the graph into layers, such that the problem can be solved optimally on each layer, then combine the solutions from each layer in a reasonable way that will result in a feasible solution. This technique has given PTASs for the following problems: subgraph isomorphism, maximum independent set, minimum vertex cover, minimum dominating set, minimum edge dominating set, maximum triangle matching, and many others. The bidimensionality theory of Erik Demaine, Fedor Fomin, Hajiaghayi, and Dimitrios Thilikos and its offshoot ''simplifying decompositions'' (,) generalizes and greatly expands the applicability of Baker's technique for a vast set of problems on planar gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' (''JACM'') is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are i ...'' References External links * {{DEFAULTSORT:Journal Of The Acm Academic journals established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNRS Conjecture
In theoretical computer science and metric geometry, the GNRS conjecture connects the theory of graph minors, the stretch factor of embeddings, and the approximation ratio of multi-commodity flow problems. It is named after Anupam Gupta, Ilan Newman, Yuri Rabinovich, and Alistair Sinclair, who formulated it in 2004. Formulation One formulation of the conjecture involves embeddings of the shortest path distances of weighted undirected graphs into \ell_1 spaces, real vector spaces in which the distance between two vectors is the sum of their coordinate differences. If an embedding maps all pairs of vertices with distance d to pairs of vectors with distance in the range d,Cd/math> then its stretch factor or distortion is the ratio C/c; an isometry has stretch factor one, and all other embeddings have greater stretch factor. The graphs that have an embedding with at most a given distortion are closed under graph minor operations, operations that delete vertices or edges from a gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the ''SIAM Journal on Matrix Analysis and Applications'', to replace the '' SIAM Journal on Algebraic and Discrete Methods''. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.57. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor of 0.755. Although its official ISO abbreviation is ''SIAM J. Discrete Math.'', its publisher and contributors frequently use the shorter abbreviation ''SIDMA''. References External links * Discrete mathematics journals Academic journals established in 1988 English-language journals Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courcelle's Theorem
In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth. The result was first proved by Bruno Courcelle in 1990 and independently rediscovered by . It is considered the archetype of algorithmic meta-theorems... Formulations Vertex sets In one variation of monadic second-order graph logic known as MSO1, the graph is described by a set of vertices and a binary adjacency relation \operatorname(.,.), and the restriction to monadic logic means that the graph property in question may be defined in terms of sets of vertices of the given graph, but not in terms of sets of edges, or sets of tuples of vertices. As an example, the property of a graph being colorable with three colors (represented by three sets of vertices R, G, and B) may be defined by the monadic second-order formula \begin \exists R\ \exists G\ \exists B\ \Bigl( & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
