摘要
如果对于G中任意和V|(G)|有相同奇偶性的独立集I,G-I有完美匹配,则称图G是ID-因子临界图,给出了3-正则的ID-因子临界图的刻画.
G is ID-factor-critical if for every independent set I of G which has the same parity with V|(G)|,G-I has a perfect matching. The 3-regular ID-factor-critical Graphs are characterized.
引文
[1]BONDY J A,MURTY S R.Graph theory with applications[M].London:Macmillan Press Ltd,1976.
[2]于青林,刘桂真.图的因子和匹配可扩性[M].北京:高等教育出版社,2010.
[3]PETERSEN J.Die theorie der regul?ren[J].Aeta Math,1891,15:193-220.
[4]TUTTE W T.The factorizations of linear graphs[J].London Math Soc,1947,22:107-111.
[5]TUTTE W T.The factors of graphs[J].Can J Math,1952(4):314-328.
[6]LOVáSZ.Subgraphs with prescribed valancies[J].J Comb Theory Ser B,1970(9):391-416.
[7]YUAN Jinjiang.Independent-set-deletable factor-critical power graphs[J].Acta Mathematica Scientia,2006,26B(4):577-584.
[8]LIU Yan.The degree conditions of ID-factor-critical graphs[J].Southest Asian Bulletin of Mathematics,2003,27:641-648.
[9]LIANG Caixia,LIU Yan.The degree sum conditions of ID-factor-critical Graphs[J].Chinese Journal of Engineering Mathematics,2006,23:169-174.
[10]马芳,刘岩.独立集可削去的因子临界图和无爪的独立集可削去因子临界图的度条件[J].华南师范大学学报(自然科学版),2008(2):29-33.
[11]MA Fang,LIU Yan.ID-factor-critical and claw-free graphs of diameter 2[J].Southeast Asian Bulletin of Math,2009,33:879-883.
[12]LIANG Caixia,LIU Yan.ID-factor-critical claw-free Graphs[J].Pacific Journal of Applied Mathematics,2013,4(5):253-258.