<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: arial,helvetica,sans-serif; font-size: 10pt; color: #000000'>Katherine Edwards will present her research seminar/general exam on Friday <br>May 10 at 2PM in room 302. The members of her committee are: Paul <br>Seymour (Math) advisor, Moses Charikar, and Mark Braverman. Everyone is <br>invited to attend her talk and those faculty wishing to remain for the oral exam <br>following are welcome to do so. Her abstract and reading list follow below.<br>-----------------------------<br><br>Edge-coloring 7- and 8-regular planar graphs<br><br>In 1974, Seymour conjectured the following: Let G be a k-regular planar (multi)graph,<br>such that for every odd set X of vertices of G, at least k edges of G have one end in X<br>and the other in V (G) nX. Then G is k-edge-colorable. For k = 3 this is equivalent to<br>the four-color theorem. The cases k = 4; 5 were solved by Guenin, the case k = 6 by<br>Dvorak, Kawarabayashi and Kral, and the case k = 7 by Edwards and Kawarabayashi.<br>In joint work with Chudnovsky and Seymour, we now have a proof for the case k = 8,<br>and that is the topic of this talk.<br><br>Reading list<br><br>[1] Paolo Codato, Michele Conforti, and Claudia Sera ni. Packing t-joins. Journal of Graph<br>Theory, 22(4):293{296, 1996.<br><br>[2] WJ Cook, WH Cunningham, WR Pulleyblank, and A Schrijver. Combinatorial Opti-<br>mization. 1998. New York, NY: Wiley-Interscience.<br><br>[3] Bertrand Guenin. Packing t-joins and edge colouring in planar graphs. 2003.<br><br>[4] Penny Haxell and Jessica McDonald. On characterizing vizing's edge colouring bound.<br>Journal of Graph Theory, 69(2):160-168, 2012.<br><br>[5] Takao Nishizeki and Kenichi Kashiwagi. On the 1.1 edge-coloring of multigraphs. SIAM<br>Journal on Discrete Mathematics, 3(3):391-410, 1990.<br><br>[6] Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas. The four-colour<br>theorem. Journal of Combinatorial Theory, Series B, 70(1):2 -44, 1997.<br><br>[7] P.D. Seymour. The matroids with the max-flow min-cut property. Journal of Combina-<br>torial Theory, Series B, 23(2-3):189-222, 1977.<br><br>[8] P.D. Seymour. On multi-colourings of cubic graphs, and conjectures of fulkerson and<br>tutte. Proc. London Math. Soc, 38(3):423-460, 1979.<br><br>[9] P.D. Seymour. On odd cuts and plane multicommodity flows. Proceedings of the London<br>Mathematical Society, 3(1):178-192, 1981.<br></div></body></html>