On plane bipartite graphs without fixed edges
Applied Mathematics Letters, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khaled Salem, Sandi Klavžar
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2-resonance of plane bipartite graphs and its applications to boron–nitrogen fullerenes
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heping Zhang
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The rotation graphs of perfect matchings of plane bipartite graphs
Discrete Applied Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heping Zhang, Fuji Zhang
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Complete bipartite graphs flexible in the plane
Sbornik: Mathematics, 2023 A complete bipartite graph $K_{3,3}$, considered as a planar linkage with joints at the vertices and with rods as edges, is in general inflexible, that is, it admits only motions as a whole. Two types of its paradoxical mobility were found by Dixon in 1899. Later on, in a series of papers by several different authors the question of the flexibility of $
Kovalev, Mikhail D., Orevkov, Stepan Yu.
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Matching transformation graphs of cubic bipartite plane graphs
Discrete Mathematics, 2003 If \(M\) is any perfect matching of a connected cubic bipartite plane graph \(G\), then the authors prove that \(G\) has at least two disjoint \(M\)-alternating faces. This result is best possible in the sense that there are such graphs which do not have three disjoint \(M\)-alternating faces for some perfect matching \(M\).
Sheng Bau, Michael A. Henning
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1-factors and characterization of reducible faces of plane elementary bipartite graphs
Discussiones Mathematicae Graph Theory, 2012 As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekule structures (1-factors). A bipartite graph G is called elementary if G is connected and every edge belongs to a 1-factor of G. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face f of a
Andrej Taranenko, Aleksander Vesel
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A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sandi Klavžar, Khaled Salem
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Combinatorics of perfect matchings in plane bipartite graphs and application to tilings
Theoretical Computer Science, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J.C. Fournier, Fournier, J.C.
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Plane subgraphs in geometric complement of 2-factor and complete bipartite geometric graph
Electronic Notes in Discrete Mathematics, 2006 Abstract In this article we study when there exist non-crossing subgraphs in a geometric complement of 2-factor and in a complete bipartite geometric graph.
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A Sufficient Condition for Cubic 3‐Connected Plane Bipartite Graphs to be Hamiltonian
Journal of Graph TheoryABSTRACTBarnette's conjecture asserts that every cubic 3‐connected plane bipartite graph is hamiltonian. Although, in general, the problem is still open, some partial results are known. In particular, let us call a face of a plane graph big (small) if it has at least six edges (it has four edges, respectively). Goodey proved for a 3‐connected bipartite
Florek, Jan
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