?ュ??瀛﹁??锛???浣冲??nbsp;????

?ュ??????浣?锛???寮?澶у?

?ュ???堕?达?2024骞???12?ワ??ㄤ?锛?涓???9:30--10:30

?ュ???扮?癸?瀛︽椿浼?璁??

?ュ????瑕?锛?A signed graph is a graph in which each edge receives a positive or a negative sign. In a signed graph, a sign circuit is either a balanced circuit or a barbell. A signed graph is called flow-admissible if each edge lies in a sign circuit. In this talk, we shall discuss circuit k-cover and shortest circuit cover problems of signed graphs. Motived by Prof. Fan??s classical 6-cover theorem of graphs, we use some flow cover/decomposition techniques to study the circuit cover problem of signed graphs. We show that the circuit cover problem of signed graphs can be reduced to the cubic case in some sense, i.e., if for every cubic graph G, the signed graph (G, -) admits a circuit k-cover, then we can obtain circuit 12k-covers for all flow-admissible signed graphs. Moreover, we show that every flow-admissible signed planar graph admits a circuit 12-cover, whose proof utilizes the 4CT. Using similar ideas, we also connect this problem to the Berge-Fulkerson Conjecture of cubic graphs. 

绠?浠?锛? ??浣冲?诧???寮?澶у??板?绉?瀛﹀????????锛???澹???瀵煎????????纭?澹??涓?浜?涓??界?瀛︽????ぇ瀛︼?绠?浠?锛???澹??涓?浜?缇??借タ寮???灏间?澶у?锛?瀵煎?涓鸿??瑰缓????锛?锛?涔????ヨ????寮?澶у?锛???浠昏?甯?????????锛?2022骞?2???充?浠绘??????涓昏???绌跺?磋叮????ｆ?板?涓?缁????捐????????剧?????诧?Tutte?存?版???璁猴??剧???涓???瑙ｏ????х???锛?缃?缁?涓?缁???浼???绛??????宸插???????琛ㄨ???涓???浣?绡?锛???绌舵??????琛ㄥ??. Combin. Theory Ser. B, SIAM J. Discrete Math, J. Graph Theory 绛???蹇?????浠诲ぉ娲ュ??板?浼?绉?涔﹂?匡?涓??借?绛瑰?浼??捐?缁?????浼???浜?锛?浠ュ??SCI??蹇?Journal of Combinatorial Optimization?????杈?锛?Associate Editor锛?绛?瀛︽???艰?????ラ??澶╂触甯???131?????板??浜烘???瑰?诲伐绋?绗??灞?娆?2019)锛?澶╂触甯???骞翠汉????涓惧伐绋?(2020)锛???寮?澶у??惧????骞村?绉?甯﹀ご浜哄?瑰?昏???(2021)??2022骞磋?峰?藉????剁?瀛﹀?洪??浼?绉???骞寸?瀛﹀?洪??椤圭????┿??