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Debsoumya Chakraborti, Rainbow matchings in edge-colored simple graphs

Tuesday, December 1, 2020 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

There has been much research on finding a large rainbow matching in a properly edge-colored graph, where a proper edge coloring is a coloring of the edge set such that no same-colored edges are incident. Barát, Gyárfás, and Sárközy conjectured that in every proper edge coloring of a multigraph (with parallel edges allowed, but not loops) with $2q$ colors where each color appears at least $q$ times, there is always a rainbow matching of size $q$. We prove that $2q + o(q)$ colors are enough if the graph is simple, confirming the conjecture asymptotically for simple graphs. We also make progress in the lower bound on the required number of colors for simple graphs, which disproves a conjecture of Aharoni and Berger. We use a randomized algorithm to obtain a large rainbow matching, and the analysis of the algorithm is based on differential equations method. We will also briefly comment on the limitations of using our probabilistic approach for the problem. This talk will be based on a joint work with Po-Shen Loh.


Tuesday, December 1, 2020
4:30 PM - 5:30 PM KST
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Room B232
IBS (기초과학연구원)


Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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