Course Recommendation Model Based on Layer Dropout Graph Differential Contrastive Learning by Yong Ouyang, Hao Long, Rong Gao, Jinghang Liu

“…At present, the course recommendation model of graph collaborative filtering mainly uses bipartite graph modeling to obtain user-course cooperative relationship. …”
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On the Distribution of non-attacking Bishops on a Chessboard C by Shanaz Ansari Wahid

“…It is shown how the placement of non-attacking bishops on a chessboard C is related to the matching polynomial of a bipartite graph. Reduction algorithms for finding the bishop polynomial of C are given. …”
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Combinatorial scientific computing / by Naumann, Uwe, 1969-, Schenk, Olaf, 1967-

“…Several discrete combinatorial problems and data structures, such as graph and hypergraph partitioning, supernodes and elimination trees, vertex and edge reordering, vertex and edge coloring, and bipartite graph matching, arise in these contexts. As an example, parallel partitioning tools can be used to ease the task of distributing the computational workload across the processors. …”

MindTheDApp: A Toolchain for Complex Network-Driven Structural Analysis of Ethereum-Based Decentralized Applications by Giacomo Ibba, Sabrina Aufiero, Silvia Bartolucci, Rumyana Neykova, Marco Ortu, Roberto Tonelli, Giuseppe Destefanis

“…The bipartite graph generated by the proposed tool comprises two sets of nodes: one representing smart contracts, interfaces, and libraries, and the other including functions, events, and modifiers. …”
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Sidorenko's conjecture, colorings and independent sets by Csikvari, Peter, Lin, Zhicong

“…For instance, for a bipartite graph H the number of q-colorings ch(H, q) satisfies ch(H, q) ≥ q[superscript v(H)](q − 1/q)[superscript e(H)]. …”
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Ultra-scalable spectral clustering and ensemble clustering by Huang, Dong, Wang, Chang-Dong, Wu, Jiansheng, Lai, Jian-Huang, Kwoh, Chee-Keong

“…By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. …”
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On a problem of El-Zahar and Erdős by Nguyen, T, Scott, A, Seymour, P

“…This, together with excluding <i>K_t</i>, is <i>not</i> enough to guarantee two anticomplete subgraphs both with large minimum degree; but it works if instead of excluding <i>K_t</i> we exclude the complete bipartite graph <i>K_t,t</i>. More exactly: for all <i>t</i>, <i>c</i> ≥ 1 there exists <i>d</i> ≥ 1 such that if <i>G</i> has minimum degree at least <i>d</i>, and does not contain the complete bipartite graph <i>K_t,t</i> as a subgraph, then there are two anticomplete subgraphs both with minimum degree at least <i>c</i>.…”

On the Number of α-Labeled Graphs by Barrientos Christian, Minion Sarah

“…When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an α-labeling. …”
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Bisplit graphs satisfy the Chen-Chv\'atal conjecture by Laurent Beaudou, Giacomo Kahn, Matthieu Rosenfeld

“…A graph is bisplit if its vertex set can be partitioned into three stable sets with two of them inducing a complete bipartite graph. We prove that these graphs satisfy the Chen-Chv\'atal conjecture: their metric space (in the usual sense) has a universal line (in an unusual sense) or at least as many lines as the number of vertices.…”
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ABC energies and spectral radii of some graph operations by Ahmad Bilal, Muhammad Mobeen Munir

“…The present article presents some new results relating to Atomic Bond Connectivity energies and Spectral radii of generalized splitting and generalized shadow graphs constructed on the basis of some fundamental families of cycle graph Cn, complete graph Kn and complete bipartite graph Kn,n referred as base graphs. In fact we relate the energies and Spectral radii of splitting and shadow graphs with the energies and Spectral radii of original graphs.…”
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Eulerian and Even-Face Graph Partial Duals by Metrose Metsidik

“…Eulerian and bipartite graph is a dual symmetric concept in Graph theory. …”
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Polynomial bounds for chromatic number. I: excluding a biclique and an induced tree by Scott, A, Seymour, P, Spirkl, S

“…It was proved by Rodl that graphs that do not contain H as an induced subgraph, and do not contain the complete bipartite graph $K_{t,t}$ as a subgraph, have bounded chromatic number. …”

BgNet: Classification of benign and malignant tumors with MRI multi-plane attention learning by Hong Liu, Meng-Lei Jiao, Meng-Lei Jiao, Xiao-Ying Xing, Han-Qiang Ou-Yang, Han-Qiang Ou-Yang, Han-Qiang Ou-Yang, Yuan Yuan, Jian-Fang Liu, Yuan Li, Chun-Jie Wang, Ning Lang, Yue-Liang Qian, Liang Jiang, Liang Jiang, Liang Jiang, Hui-Shu Yuan, Xiang-Dong Wang

“…In a bipartite graph structure, the tumor area in each plane is used as the vertex of the graph, and the matching between different planes is used as the edge of the graph. …”
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On Some Properties of Antipodal Partial Cubes by Polat Norbert

“…We prove that an antipodal bipartite graph is a partial cube if and only it is interval monotone. …”
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Generalized commutativity degrees of some finite groups and their related graphs by Abdul Hamid, Muhanizah

“…The last graph is the bipartite graph associated to a non-nilpotent group of class (n - 1), called as relative non-nil (n - 1) bipartite graph. …”
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Connectivity of Random Geometric Hypergraphs by Henry-Louis de Kergorlay, Desmond J. Higham

“…We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. …”
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Formalizing Randomized Matching Algorithms by Dai Tri Man Le, Stephen A. Cook

“…The first algorithm is for testing if a bipartite graph has a perfect matching, and is based on the Schwartz-Zippel Lemma for polynomial identity testing applied to the Edmonds polynomial of the graph. …”
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Topics in extremal graph theory and probabilistic combinatorics by Roberts, A

“…</p> <p>A <em>matching</em> in a bipartite graph G = (U, V, E) is a subset of the edges where no two edges meet, and each vertex from U is in an edge. …”

Alpha Labeling of Amalgamated Cycles by Christian Barrientos

“…A graceful labeling of a bipartite graph is an \a-labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set. …”
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Conditional risk measures in a bipartite market structure by Kley, O, Klueppelberg, C, Reinert, G

“…We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. …”