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{{Short description|Abstraction of 2-colorable graphs}} In mathematics, a '''bipartite matroid''' is a [[matroid]] all of whose circuits have [[even number|even]] ...

{{Short description|Planar bipartite graph with 25 vertices and 31 edges}} | properties = [[Bipartite graph|Bipartite]]<br>[[Planar graph|Planar]] ...

...}}</ref> The problem is [[NP-hard]] even in the class of [[Bipartite graph|bipartite]] and [[planar graph]]s.<ref>{{harvnb|Yannakakis|1981}}</ref> ...for computing a 4/3-approximation of the dissociation number in bipartite graphs was published in 2022.<ref>{{harvnb|Hosseinian|Butenko|2022}}</ref> ...

{{Short description|Graph whose nodes are one of the vertex sets of a bipartite graph}} ...i-4-cube.svg|thumb|240px|The halved cube graph of order 4, obtained as the bipartite half of an order-4 [[hypercube graph]]]] ...

...umb|400px|The sequences above are able to be the degree sequence for the [[bipartite graph]] below it, where each vertex has a [[degree (graph theory)|degree]] ...(b_1,\dots,b_m)</math> is the [[bipartite graph|degree sequence]] of this bipartite graph. ...

...An <math>O(VE)</math> algorithm for ear decompositions of matching-covered graphs|journal=ACM Transactions on Algorithms|volume=1|issue=2|pages=324–337|doi=1 ...women. Given the preferences of the candidates, the agency constructs a [[bipartite graph]] where there is an edge between a man and a woman if they are compat ...

...on <math>\ell</math> but not depend on the choice of vertex. Walk-regular graphs can be thought of as a [[spectral graph theory]] analogue of [[vertex-trans ...et/a/264155|title=Are there only finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular?|website=mathoverfl ...

| properties = [[Cubic graph|Cubic]]<br>[[Bipartite graph|Bipartite]] ...ltonian graph|Hamiltonian]].<ref>Tutte, W. T. "On the 2-Factors of Bicubic Graphs." Discrete Math. 1, 203-208, 1971/72.</ref><ref>Bondy, J. A. and Murty, U. ...

...tonian graph|Hamiltonian]]<br>[[planar graph|Planar]]<br>[[Bipartite graph|Bipartite]] ...993.</ref><ref>Noy, M. and Ribó, A. "Recursively Constructible Families of Graphs." Adv. Appl. Math. 32, 350-363, 2004.</ref> ...

| year = 1997}}.</ref> or '''semiregular bipartite graph'''<ref>{{citation | year = 2009}}.</ref> is a [[bipartite graph]] <math>G=(U,V,E)</math> for which every two vertices on the same sid ...

...ding of an information source having ambiguous alphabet and the entropy of graphs.|journal=6th Prague Conference on Information Theory|pages= 411–425}}</ref> ...G. Simonyi, "Perfect graphs and graph entropy. An updated survey," Perfect Graphs, John Wiley and Sons (2001) pp. 293-328, Definition 2”</ref> ...

{{short description|Derived bipartite graph with twice as many nodes as the original graph}} ...''Kronecker double cover''', '''canonical double cover''' or simply the '''bipartite double''' of {{mvar|G}}. ...

...folded cubes of odd dimension are examples of [[odd graph|generalized odd graphs]].<ref>{{harvtxt|Van Dam|Haemers|2010}}.</ref> When ''k'' is odd, the [[bipartite double cover]] of the dimension-''k'' folded cube is the dimension-''k'' cu ...

...iltonian]]<br>[[Semi-symmetric graph|Semi-symmetric]]<br>[[Bipartite graph|Bipartite]] ...gs of Famous Graphs"].</ref><ref>Pegg, E. T. and Exoo, G. "Crossing Number Graphs." Mathematica J. 11, 2009.</ref> ...

[[File:Conjugate-dessins.svg|thumb|Two non-isomorphic graphs realized from the degree sequence (3, 2, 2, 2, 2, 1, 1, 1).]] | title = A remark on the existence of finite graphs ...

==Relation to Eulerian graphs== ...le cycles, from which it follows that the [[graphic matroid]]s of Eulerian graphs are examples of Eulerian matroids.<ref name="w69">{{citation ...

...ein Ore]].<ref>{{Cite journal|last=Ore|first=Oystein|date=1955-12-01|title=Graphs and matching theorems|url=https://projecteuclid.org/euclid.dmj/1077466548|j Suppose ''G'' is a [[bipartite graph]], with bipartition ''V'' = ''X'' ∪ ''Y''. The '''deficiency''' of '' ...

...name=HamiltonianGraph|title=Hamiltonian Graph}}</ref><br>[[Bipartite graph|Bipartite]]<br>[[Perfect graph|Perfect]]<br>[[Eulerian graph|Eulerian]]<br>[[1-walk r ...R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.</ref> ...

...problem]]. The second and third one are equivalent and are known as the [[bipartite realization problem]]. {{harvtxt|Chen|1966}} gives a characterization for [ ...Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs ...

...not interval colorable by Sevast’janov though the interval colorability of graphs with maximum degree lying between four and twelve is still unknown. ...ular graphs.[[bipartite graph]]s which are regular and not regular, planar graphs, among the other extensions that has been initiated in interval edge colori ...