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A remark on embedded bipartite graphs

Gadi Moran
1987 Journal of combinatorial theory. Series B (Print)  
B 32 (1982), 95-98 ) is replaced by an elementary argument on permutations. 0 1987 Academic Press, Inc Let 5' be an orientable compact surface, and let G be a finite bipartite graph with u vertices, 2-  ...  Let m denote the number of 4k-gonal faces (k = 1, 2, 3,...) of this embedding (a face is a connected component of the complement of the graph G in S; G is 2-cell embedded means that every face is homeomorphic  ...  Let 5' be an orientable compact surface, and let G be a finite bipartite graph with u vertices, 2-cell embedded in S.  ... 
doi:10.1016/0095-8956(87)90023-2 fatcat:pnuqdaflvzfsrokji2jbr5wauu

Graphs Embedded into Finite Projective Planes [article]

Keith Mellinger, Ryan Vaughn, Oscar Vega
2013 arXiv   pre-print
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs.  ...  We also make connections between embeddings of graphs and the existence of certain substructures in a plane, such as Baer subplanes and arcs.  ...  Remark 3. If a graph G is embedded in a projective plane π, then G can also be embedded in any other plane that is isomorphic to π, or in one that has a subplane isomorphic to π.  ... 
arXiv:1310.0196v1 fatcat:rdthdbfp4zhw7fwid2nc5i7kza

Bipartite partial duals and circuits in medial graphs

Stephen Huggett, Iain Moffatt
2013 Combinatorica  
We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.  ...  It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs.  ...  The statement is true in the other direction since the dual of any bipartite embedded graph is Eulerian (see Remark 3).  ... 
doi:10.1007/s00493-013-2850-0 fatcat:zn6vdo2r2rdp5gjf7gvhunbqwe

Irregular embeddings of multigraphs with fixed chromatic number

Michael S. Jacobson, Jenö Lehel
1995 Discrete Mathematics  
Let G be a c-chromatic multigraph (c >t 2) with maximum edge multiplicity s.  ...  In this note we show that G has an embedding as an induced subgraph, into some degree irregular c-chromatic multigraph having the same maximum edge multiplicity. * Corresponding author.  ...  An immediate corollary of Theorem 3 (with c = 2) is a result or irregular embedding of bipartite graphs communicated in [1, Theorem 11].  ... 
doi:10.1016/0012-365x(94)00042-h fatcat:acdmr3horffjzcq7q7dmwa7owa


Dongseok Kim
2014 Honam Mathematical Journal  
As applications, we prove that every link L is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph K_2,n, where all voltage assignments on the edges  ...  We study the Seifert surfaces of a link by relating the embeddings of graphs by using induced graphs.  ...  Let us remark that by flipping two discs corresponding to vertices in one of the bipartition sets whose cardinality is 2, Corollary 3.4 can be restated that for a given link L, there exists a graph diagram  ... 
doi:10.5831/hmj.2014.36.2.399 fatcat:nu7submphvf2pl5e7qqo5spxgi

Bipartite graphs and their dessins d'enfants [article]

Ruben A. Hidalgo
2017 arXiv   pre-print
Each finite and connected bipartite graph induces a finite collection of non-isomorphic dessins d'enfants, that is, 2-cell embeddings of it into some closed orientable surface.  ...  Remark 9 (Clean bipartite graphs).  ...  Remark 2. A 2-cell embedding ι : G ֒→ X induces a natural 2-cell embedding ι : G clean ֒→ X.  ... 
arXiv:1611.02901v2 fatcat:mdpejrscbvdsnhwo26t7f57iey

Eulerian and bipartite binary delta-matroids [article]

Qi Yan, Xian'an Jin
2020 arXiv   pre-print
Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is bipartite if and only if its Petrie dual is orientable.  ...  The dual of any bipartite embedded graph is Eulerian. We also extend the result from embedded graphs to the class of delta-matroids that arise as twists of binary matroids.  ...  This fact only holds for general embedded graphs in one direction: the dual of any bipartite embedded graph is Eulerian. And it is not true in other direction in general.  ... 
arXiv:2003.02125v1 fatcat:krki2ygnnfefbbyca7uzmyjpvq

Amalgams of Cubic Bipartite Graphs

Domenico Labbate
2004 Designs, Codes and Cryptography  
We define a "graph amalgam" to point out a different approach to certain classes of cubic bipartite graphs.  ...  Furthermore, we find relations between graph amalgams, 3-bridges and star-products of cubic bipartite graphs.  ...  Conversely, every bipartite k-regular graph on 2n vertices can be seen as a symmetric configuration n k , up to duality.  ... 
doi:10.1023/b:desi.0000029229.06512.83 fatcat:wd6yuofpdzdjper27dligiy4da

Volumes and Tangent Cones of Matroid Polytopes [article]

David C. Haws
2011 arXiv   pre-print
To prove this result, we provide a triangulation in which the maximal simplicies are in bijection with the spanning thrackles of the complete bipartite graph K_r,n-r.  ...  We show here that for the uniform matroid of rank r on n elements, the number of simplicial cones in any triangulation of a tangent cone is n-2 r-1.  ...  Let K s,t be the complete bipartite graph with the planar embedding in Remark 7.  ... 
arXiv:1109.4453v1 fatcat:lee4ahv2mnbrpbfjedsbv5wpgm

Matching through Embedding in Dense Graphs [article]

Nitish K. Panigrahy, Prithwish Basu, Don Towsley
2020 arXiv   pre-print
In particular, using existing network embedding techniques, we first find a low dimensional representation of the graph vertices in R^d and then run faster available matching algorithms on the embedded  ...  In this paper, we propose a novel network embedding based heuristic algorithm to solve various matching problems in dense graphs.  ...  For instance, MCM on a non-Euclidean non-bipartite complete graph runs in O(n 3 ) time where as MCM on a Euclidean non-bipartite complete graph runs in O(n 1.5 log n) time.  ... 
arXiv:2011.06767v1 fatcat:hfgbx3dmcrg7beqdwf7yxy3bue

Maximum and minimum degree conditions for embedding trees [article]

Guido Besomi and Matías Pavez-Signé and Maya Stein
2020 arXiv   pre-print
The proof of the approximate result relies on a second result, which we believe to be interesting on its own.  ...  Namely, we can embed any bounded degree tree into host graphs of minimum/maximum degree asymptotically exceeding k/2 and 4/3k, respectively, as long as the host graph avoids a specific structure.  ...  The host graph is the same, with slightly adjusted size of the sets A i .  ... 
arXiv:1808.09934v3 fatcat:s76yymzmhzc7lnonvnuroenxjm

Symmetry and the Ramsey Degrees of Finite Relational Structures

Willem L. Fouché
1999 Journal of combinatorial theory. Series A  
We show for classes of finite relational structures, including graphs, binary posets, and bipartite graphs, how this measure depends on the symmetries of the structure. 1999 Academic Press In this paper  ...  /: [C, A] Ä r, there is some copy B$ of B in C such that / assumes at most t(A) values on [B$, A].  ...  Every bipartite graph can be embedded into one which is symmetric. By this remark, together with Theorem 3.3, we can find for each ? in the orbit space P associated with G some binary poset Q ?  ... 
doi:10.1006/jcta.1998.2910 fatcat:e75ff3gsbzfsfdte7wqfhvj4ha

Generalized Thrackle Drawings of Non-bipartite Graphs

Grant Cairns, Yury Nikolayevsky
2008 Discrete & Computational Geometry  
In a previous paper, we showed that a bipartite graph G can be drawn as a generalized thrackle on an oriented closed surface M if and only if G can be embedded in M.  ...  In this paper, we use Lins' notion of a parity embedding and show that a non-bipartite graph can be drawn as a generalized thrackle on an oriented closed surface M if and only if there is a parity embedding  ...  Clearly, if a graph G is not bipartite, the image of a parity embedding of G lies on a non-orientable surface.  ... 
doi:10.1007/s00454-008-9095-5 fatcat:voixjsugpzfgthxowxhyz5rooe

On dispersability of some products of cycles [article]

Samuel S. Joslin, Paul C. Kainen, Shannon Overbay
2021 arXiv   pre-print
We show that the matching book thickness of the Cartesian product of two odd-length cycle-graphs is five if at least one of the cycles has length 3 or 5.  ...  We conclude in Section 4 with some remarks on further applications of our methods to graphs with a repetitive structure.  ...  Remarks We have given a five stack layout [6] of a toroidal grid (circumference 3 or 5) where at most one process starts or ends at a single time step in each stack.  ... 
arXiv:2108.11839v1 fatcat:mdk4tl3rerfvfnbl7245bxexji

Minrank of Embedded Index Coding Problems and its Relation to Connectedness of a Bipartite Graph [article]

Anjana A Mahesh, B. Sundar Rajan
2022 arXiv   pre-print
bipartite graph of a single unicast embedded index coding problem (SUEICP).  ...  A graphical representation for an EICP is given using directed bipartite graphs, called bipartite problem graph, and the side information alone is represented using an undirected bipartite graph called  ...  The bipartite problem graph of the EICP in Example 1 is given in Fig. 1(a ) and the corresponding side information bipartite graph is given in Fig. 1(b) . Remark 2.  ... 
arXiv:2201.08680v1 fatcat:3y2cftvfvfavlhqlkscpy7b3pq
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