What are...transversal matroids?

Goal. Explaining basic concepts in the intersection of graph theory and algebra in an intuitive way. This time. What are...transversal matroids? Or: More examples from graph theory. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Disclaimer. Graph theory is one of the most applicable fields of mathematics, essentially by birth, but also a very wide area of beautiful results and active research. So to be precise, this video series is mostly about the interaction between graphs, matrices and polynomials and their various friends. That is, algebraic methods are applied to problems regarding graphs, and potentially also the other way around. Warning. There are some mistakes, see the comments for details. Thanks everyone! Slides. http://www.dtubbenhauer.com/youtube.html TeX files for the presentation. https://github.com/dtubbenhauer/My-TeX-files Website with exercises. http://www.dtubbenhauer.com/lecture-algebragraph-2023.html Thumbnail. A modification of https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Star_network_7.svg/1200px-Star_network_7.svg.png Algebraic graph theory. https://en.wikipedia.org/wiki/Algebraic_graph_theory https://en.wikipedia.org/wiki/Adjacency_matrix https://en.wikipedia.org/wiki/Laplacian_matrix https://en.wikipedia.org/wiki/Spectral_graph_theory https://en.wikipedia.org/wiki/Tutte_polynomial https://en.wikipedia.org/wiki/Chromatic_polynomial https://en.wikipedia.org/wiki/Bollob%C3%A1s%E2%80%93Riordan_polynomial https://en.wikipedia.org/wiki/Graph_property Graph theory. https://en.wikipedia.org/wiki/Graph_(discrete_mathematics) https://en.wikipedia.org/wiki/Graph_(abstract_data_type) https://en.wikipedia.org/wiki/List_of_graph_theory_topics https://en.wikipedia.org/wiki/Network_theory https://en.wikipedia.org/wiki/Tree_(graph_theory) https://en.wikipedia.org/wiki/Graph_coloring https://en.wikipedia.org/wiki/List_of_algorithms#Graph_algorithms Applications of (algebraic) graph theory. https://www.zib.de/groetschel/teaching/WS1314/BondyMurtyGTWA.pdf https://link.springer.com/book/10.1007/978-1-4612-0933-1 https://link.springer.com/book/10.1007/978-94-009-7154-7 https://people.unipmn.it/fragnelli/dispense/Chimica/Balaban.pdf https://koreascience.kr/article/JAKO200709649107854.pdf https://math.stackexchange.com/questions/1402260/applications-of-algebraic-graph-theory https://math.stackexchange.com/questions/2568508/are-there-any-applications-of-algebraic-graph-theory-to-computer-science https://math.stackexchange.com/questions/1660962/applications-of-graph-theory-to-algebra https://en.wikipedia.org/wiki/PageRank https://en.wikipedia.org/wiki/List_of_important_publications_in_mathematics#Graph_theory https://towardsdatascience.com/what-is-graph-theory-and-why-should-you-care-28d6a715a5c2 https://www.xomnia.com/post/graph-theory-and-its-uses-with-examples-of-real-life-problems/ Pictures used. https://i.imgur.com/68rQFhB.png A modification of https://i.imgur.com/68rQFhB.png https://upload.wikimedia.org/wikipedia/commons/e/e1/Cube_graph.png https://mathworld.wolfram.com/images/eps-svg/PerfectMatching_1000.svg Modifications of https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Star_network_7.svg/1200px-Star_network_7.svg.png https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Star_network_7.svg/1200px-Star_network_7.svg.png Some books I am using (I sometimes steal some pictures from there). https://www.win.tue.nl/~aeb/2WF05/spectra.pdf also: https://link.springer.com/book/10.1007/978-1-4614-1939-6 https://www.math.arizona.edu/~kglasner/math443/Graphs_and_Matrices_text.pdf also: https://link.springer.com/book/10.1007/978-1-4471-6569-9 https://link.springer.com/book/10.1007/978-1-4613-0163-9 https://link.springer.com/book/10.1007/978-1-4612-0619-4 https://www.zib.de/groetschel/teaching/WS1314/BondyMurtyGTWA.pdf also: https://link.springer.com/book/9781846289699 https://www.cambridge.org/core/books/random-graphs/E21023008001CFA182CE666F5028489F https://diestel-graph-theory.com/ also: https://link.springer.com/book/10.1007/978-3-662-53622-3 https://assets.cambridge.org/97805217/67248/frontmatter/9780521767248_frontmatter.pdf Mathematica. https://reference.wolfram.com/language/tutorial/GraphDrawingIntroduction.html https://reference.wolfram.com/language/guide/GraphsAndNetworks.html https://demonstrations.wolfram.com/topic.html?limit=20&topic=Graph+Theory SageMath. https://doc.sagemath.org/html/en/reference/graphs/index.html #graphtheory #algebra #mathematics