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1. On tripartite common graphs

   https://doi.org/10.1017/S0963548322000074  

   Grzesik, Andrzej; Lee, Joonkyung; Lidický, Bernard; Volec, Jan (September 2022, Combinatorics, Probability and Computing)

   Abstract A graph $$H$$ is common if the number of monochromatic copies of $$H$$ in a 2-edge-colouring of the complete graph $$K_n$$ is asymptotically minimised by the random colouring. Burr and Rosta, extending a famous conjecture of Erdős, conjectured that every graph is common. The conjectures of Erdős and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Collecting new examples of common graphs had not seen much progress since then, although very recently a few more graphs were verified to be common by the flag algebra method or the recent progress on Sidorenko’s conjecture. Our contribution here is to provide several new classes of tripartite common graphs. The first example is the class of so-called triangle trees, which generalises two theorems by Sidorenko and answers a question of Jagger, Šťovíček, and Thomason from 1996. We also prove that, somewhat surprisingly, given any tree $$T$$ , there exists a triangle tree such that the graph obtained by adding $$T$$ as a pendant tree is still common. Furthermore, we show that adding arbitrarily many apex vertices to any connected bipartite graph on at most $$5$$ vertices yields a common graph. 

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2. On subgraphs of tripartite graphs

   https://doi.org/10.1016/j.disc.2022.113152  

   Bhalkikar, Abhijeet; Zhao, Yi (January 2023, Discrete Mathematics)
3. Tripartite-BIMA (Bangladesh-India-Myanmar Array)

   https://doi.org/10.7914/SN/XR_2018  

   Sandvol, Eric; Gaherty, Jim; Steckler, Michael; Persaud, Patricia (January 2018, International Federation of Digital Seismograph Networks)

   The seismology component of this experiment will consist of a 2.5 dimensional transect that will cross from Bangladesh into Myanmar. We will install as many stations as possible on hard rock sites to minimize noise, although this will not be possible in low-lying deltaic areas. The array will consist of three lines. The middle line will be closely spaced in order to image shallow crustal features. It will have a station spacing of 5-10 km in Bangladesh expanding to 15 km in eastern Myanmar. To image the detachment megathrust at 10-20 km depth in the accretionary prism, a 100-km-long section spanning the Bangladesh and India border will have station spacing of 5 km or less. Two flanking lines located ~40 km on either side will have ~40 km spacing. This 80 km wide swath is critical for earthquake locations and body- and surface-wave tomography. The stations will operate for ~2 years, providing ample recordings from a wide backazimuth distribution of local, regional, and teleseismic events, and ambient noise for analysis 

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4. Analysis of a tripartite entanglement distribution switch

   https://doi.org/10.1007/s11134-021-09731-w  

   Nain, Philippe; Vardoyan, Gayane; Guha, Saikat; Towsley, Don (August 2022, Queueing Systems)
5. Uncovering a tripartite landmark in posterior cingulate cortex

   https://doi.org/10.1126/sciadv.abn9516  

   Willbrand, Ethan H.; Parker, Benjamin J.; Voorhies, Willa I.; Miller, Jacob A.; Lyu, Ilwoo; Hallock, Tyler; Aponik-Gremillion, Lyndsey; Koslov, Seth R.; Bunge, Silvia A.; Foster, Brett L.; et al (September 2022, Science Advances)

   A previously uncharted brain structure links functional and anatomical organization and differs across the life span and species. 

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