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Graph able to be partitioned into multiple independent sets
multipartite graph is a graph that is complete k-partite for some k. The Turán graphs are the special case of complete multipartite graphs in which the
Multipartite_graph
sets of vertices in a tree decomposition. balanced A bipartite or multipartite graph is balanced if each two subsets of its vertex partition have sizes
Glossary_of_graph_theory
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
matching from a complete bipartite graph Complete multipartite graph, a generalization of complete bipartite graphs to more than two sets of vertices Biclique
Complete_bipartite_graph
Graph with oriented edges
complete graph with the edges replaced by pairs of inverse arcs). It follows that a complete digraph is symmetric. Semicomplete multipartite digraphs
Directed_graph
Graph with at most one crossing per edge
many graphs. A complete classification of the 1-planar complete graphs, complete bipartite graphs, and more generally complete multipartite graphs is known
1-planar_graph
Balanced complete multipartite graph
The Turán graph, denoted by T ( n , r ) {\displaystyle T(n,r)} , is a complete multipartite graph; it is formed by partitioning a set of n {\displaystyle
Turán_graph
Graph divided into two independent sets
bipartite graph whose vertices can be ordered so that the vertex neighborhoods are contiguous Multipartite graph, a generalization of bipartite graphs to more
Bipartite_graph
Methodic assignment of colors to elements of a graph
signed graphs and gain graphs. Critical graph Graph coloring game Graph homomorphism Hajós construction Mathematics of Sudoku Multipartite graph Uniquely
Graph_coloring
Graph property
{\displaystyle G,} unless G {\displaystyle G} is a cycle graph or a complete multipartite graph. If G {\displaystyle G} is strongly regular, then n ≤ 4
Distance-regular_graph
Extremal graph theory bound on clique-free graph edges
Many of the proofs involve reducing to the case where the graph is a complete multipartite graph, and showing that the number of edges is maximized when
Turán's_theorem
Graph made from disjoint union of complete graphs
graphs. They are the complement graphs of the complete multipartite graphs and the 2-leaf powers. The cluster graphs are transitively closed, and every
Cluster_graph
Concept in graph theory
regular graphs. These include the disjoint union of one or more equal-sized complete graphs, and their complements, the complete multipartite graphs with
Strongly_regular_graph
Abstract mathematical system of two types of objects and a relation between them
\bigcup _{i<j}P_{i}\times P_{j}.} The Levi graph for these structures is defined as a multipartite graph with vertices corresponding to each type being
Incidence_structure
Concept in quantum computing
also detect genuine multipartite entanglement close to graph states. Here, the graph state itself has to be genuine multipartite entangled, that is, it
Graph_state
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
Upper bound on a graph's Shannon capacity
In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász
Lovász_number
Graph layout on multiple half-planes
the graph are very unbalanced, with b > a(a − 1), the book thickness of Ka,b is exactly a. For the Turán graph T(kr,r) (a complete multipartite graph Kk
Book_embedding
of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as
Sphericity_(graph_theory)
theorem) as well as the complete bipartite graphs and complete multipartite graphs. The simplest example of a graph that is not well-colored is a four-vertex
Well-colored_graph
Generalization of linear assignment problem from two to multiple dimensions
describing the problem using graph theory: The multidimensional assignment problem consists of finding, in a weighted multipartite graph, a matching of a given
Multidimensional assignment problem
Multidimensional_assignment_problem
Graph coloring variant in graph theory
_{0}(G)\leq \chi _{\rho }(G)\leq \alpha _{0}(G)+1} For complete multipartite graphs and wheel graphs G {\displaystyle G} : χ ρ ( G ) = α 0 ( G ) + 1 {\displaystyle
Packing_coloring
Regular polytope dual to the hypercube in any number of dimensions
complete multipartite graphs, βp 2 make Kp,p for complete bipartite graph, βp 3 make Kp,p,p for complete tripartite graphs βp n creates Kpn or Turán graphs T
Cross-polytope
Quantum state
genuine multipartite entangled. Now the bound approaches 1/2 for large N {\displaystyle N} , which makes experiments for detecting genuine multipartite entanglement
Dicke_state
Graph invariant defined from axis-parallel unit cubes
K_{p(2)}} denotes the complete multipartite graph with p {\displaystyle p} parts of cardinal 2 {\displaystyle 2} . For a graph G {\displaystyle G} on n {\displaystyle
Cubicity
Form taken by the network of interconnections of a circuit
linear graph", IEEE Transactions on Circuit Theory, vol.16, iss.3, pp. 323–330, August 1969. MacMahon, Percy A., "Yoke-chains and multipartite compositions
Circuit_topology_(electrical)
Entangled state of qubits
thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster
Cluster_state
Direct sum of uniform matroids
forms a matroid if and only if G {\displaystyle G} is a complete multipartite graph, and in this case the resulting matroid is a partition matroid. The
Partition_matroid
Independent set in a graph
Haxell, Penny; Szabó, Tibor (2012). "Bounded transversals in multipartite graphs". Journal of Graph Theory. 70 (3): 318–331. doi:10.1002/jgt.20618. ISSN 1097-0118
Rainbow-independent_set
{\displaystyle K_{3,3,1,1}} -family is generated from the complete multipartite graph K 3 , 3 , 1 , 1 {\displaystyle K_{3,3,1,1}} through repeated application
Heawood_family
Deviations from local realism
nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow an interpretation with local hidden variables
Quantum_nonlocality
Property of objects inherited by all their subobjects
forests, planar, complete, complete multipartite etc. Sometimes the term "hereditary" has been defined with reference to graph minors; then it may be called
Hereditary_property
American mathematician (1949–2022)
Rodger, C. A. (June 1992). "The chromatic index of complete multipartite graphs". Journal of Graph Theory. 16 (2): 159–163. doi:10.1002/jgt.3190160207. Retrieved
Dean_G._Hoffman
Conditional independence of exchangeable observations
Parrilo, Pablo A.; Spedalieri, Federico M. (2005-01-01). "Detecting multipartite entanglement". Physical Review A. 71 (3) 032333. arXiv:quant-ph/0407143
De_Finetti's_theorem
Italian mathematician (1906–1985)
Parrilo, Pablo A.; Spedalieri, Federico M. (1 January 2005). "Detecting multipartite entanglement". Physical Review A. 71 (3) 032333. arXiv:quant-ph/0407143
Bruno_de_Finetti
weak perfect graph theorem. See Cornuéjols & Reed (1993) for the case in which the co-disconnected side of the partition is multipartite, and Roussel
Skew_partition
Graphical language for quantum processes
Coecke, Bob; Kissinger, Aleks (2010). "The Compositional Structure of Multipartite Quantum Entanglement". Automata, Languages and Programming. Lecture Notes
ZX-calculus
Networks with multiple kinds of relations
The term "fully multidimensional" has also been used to refer to a multipartite edge-labeled multigraph. Multidimensional networks have also recently
Multidimensional_network
Society, No. 119, American Mathematical Society, 1972. Gessel, Ira. Multipartite P-partitions and inner products of skew Schur functions, Combinatorics
Quasisymmetric_function
Species of bacterium
muelleri, in return, produces more complex substrates. Cicadas have a multipartite symbiostic system including vertically-transmitted "Ca. Karelsulcia"
Karelsulcia_muelleri
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
Boy/Male
Shakespearean
The Tragedy of Julius Caesar' A conspirator against Caesar.
Boy/Male
Tamil
Wonderful, Admirable
Boy/Male
Welsh
Joy.
Surname or Lastname
German
German : from a pet form of Hermann.Swedish : variant of Hassel.English : variant of Hazel.Dutch : from a derivative of a Germanic personal name, either from a compound name formed with hadu ‘strife’ as the first element, or from a derivative of Hermann (see Herman) or Hendrik (see Henry 1).
Boy/Male
Indian
Brave, A violent warrior
Male
Native American
Native American Shawnee name CATAHECASSA means "black hoof."
Girl/Female
Hindu, Indian, Traditional
Parvati
Male
Celtic
, man appointed to administer justice.
Surname or Lastname
English
English : occupational name for a seller of spices, Middle English spic(i)er (a reduced form of Old French espicier, Late Latin speciarius, an agent derivative of species ‘spice’, ‘groceries’, ‘merchandise’).Jewish (from Poland) : variant of Spitzer.
Male
Welsh
Welsh name LLŶR means "the sea." In mythology, this is the name of a god of the sea. Identified with Irish Lir.
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
MULTIPARTITE GRAPH
a.
Pertaining to, containing, derived from, or resembling, graphite.
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
n.
An instrument for recording graphically the variations of temperature, or the indications of a thermometer.
n.
Hence, any graphic or vivid delineation or description of a person; as, a portrait in words.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
a.
Divided into many parts; having several parts.
n.
A chart or graphic representation of the average distribution of rain over the surface of the earth.
n.
A mineral, a telluride of gold and silver, of a steel-gray, silver-white, or brass-yellow color. It often occurs in implanted crystals resembling written characters, and hence is called graphic tellurium.
n.
An instrument which, when applied over an artery, indicates graphically the movements or character of the pulse. See Sphygmogram.
n.
An instrument for measuring, and recording graphically, the pressure of the blood in any of the blood vessels of a living animal; -- called also kymographion.
n.
See Graphoscope.
n.
The quality or state of being graphic.
n.
Alt. of Graphicalness
a.
Alt. of Graphical
a.
Resembling graphite or plumbago.
n.
A crucible; as, a graphite pot; a melting pot.
n.
A pen-shaped pointing device used to specify the cursor position on a graphics tablet.
a.
Alt. of Graphitoidal
adv.
In a graphic manner; vividly.