Concatenating bipartite graphs by Chudnovsky, M, Hompe, P, Scott, A, Seymour, P, Spirkl, S

The chromatic profile of locally bipartite graphs by Illingworth, F

“…Here we study the chromatic profile of locally bipartite graphs. We show that every <i>n</i>-vertex locally bipartite graph with minimum degree greater than 4/7 · <i>n</i> is 3-colourable (4/7 is tight) and with minimum degree greater than 6/11 · <i>n</i> is 4-colourable. …”

Bipartite graphs with no K6 minor by Chudnovsky, M, Scott, A, Seymour, P, Spirkl, S

“…<br> But what if we restrict ourselves to bipartite graphs? The first statement remains true: for every ε > 0 there are arbitrarily large bipartite graphs with average degree at least 8 − ε and no K6 minor. …”

Bayesian nonparametric models for bipartite graphs by Caron, F

“…We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. …”

Book drawings of complete bipartite graphs by de Klerk, E, Pasechnik, D, Salazar, G

Pure pairs. IV. Trees in bipartite graphs by Scott, AD, Seymour, P, Spirkl, S

Bipartite graph reasoning GANs for person image generation by Tang, H, Bai, S, Torr, PHS, Sebe, N

“…We present a novel Bipartite Graph Reasoning GAN (BiGraphGAN) for the challenging person image generation task. …”

Bipartite graph reasoning GANs for person pose and facial image synthesis by Tang, H, Shao, L, Torr, PHS, Sebe, N

“…We present a novel bipartite graph reasoning Generative Adversarial Network (BiGraphGAN) for two challenging tasks: person pose and facial image synthesis. …”

Risk in a large claims insurance market with bipartite graph structure by Reinert, G, Kley, O, Klueppelberg, C

“…We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-atRisk and the Conditional Tail Expectation. …”

A note on induced Turán numbers by Illingworth, F

“…Their and subsequent work has focussed on $F$ being a complete bipartite graph. In this short note, we complement this focus by asymptotically determining the induced Turán number whenever $H$ is not bipartite and $F$ is not an independent set nor a complete bipartite graph.…”

On the extremal number of subdivisions by Conlon, D, Lee, J

“…More precisely, we show that if H is a C4-free bipartite graph with maximum degree 2 on one side, then there are positive constants C and δ such that every graph with n vertices and Cn3/2−δ edges contains a copy of H⁠. …”

A complexity trichotomy for approximately counting list H-colourings by Goldberg, L, Galanis, A, Jerrum, M

“…If H is an irreflexive bipartite graph or a reflexive complete graph then counting list H-colourings is trivially in polynomial time. …”

A complexity trichotomy for approximately counting list H-colourings by Galanis, A, Goldberg, L, Jerrum, M

“…If H is an irreflexive bipartite graph or a reflexive complete graph then counting list H-colourings is trivially in polynomial time. …”

Sidorenko's conjecture, graph norms, and pseudorandomness by Lee, J

“…This conjecture is closely related to Sidorenko's conjecture in the sense that it is true for every bipartite graph H that satisfies Sidorenko's conjecture. …”

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>.…”

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. …”

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. …”

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. …”

The Partner Units Problem − A Constraint Programming Case Study by Drescher, C

“…Technically it consists of partitioning a bipartite graph under side conditions. In this work we describe how constraint programming technology can be leveraged to tackle the problem. …”

Clique covers of H-free graphs by Nguyen, T, Scott, A, Seymour, P, Thomassé, S

“…It takes <i>n</i>²/4 cliques to cover all the edges of a complete bipartite graph <i>K</i>_{<i>n/2,n/2</i>}, but how many cliques does it take to cover all the edges of a graph <i>G</i> if <i>G</i> has no <i>K</i>_<i>t,t</i> induced subgraph? …”