Intrinsic Knotting of Almost Complete Partite Graphs  

作　　者：Li Yang Lei Feng-chun 

机构地区：[1]School of Science, Beijing Technology and Business University

出　　处：《Communications in Mathematical Research》2014年第2期183-192,共10页数学研究通讯（英文版）

基　　金：The Scientific Research Common Program(KM201410011006)of Beijing Municipal Com-mission of Education;the Research Foundation(QNJJ2012-26)for Youth Scholars of Beijing Technology and Business University;the NSF(1122013,1132002)of Beijing;the Importation and Development of High-caliber Talents Project(CIT&TCD201304029)of Beijing Municipal Institutions

摘　　要：Let G be a complete p-partite graph with 2 edges removed, p ≥ 7, which is intrinsically knotted. Let J represent any graph obtained from G by a finite sequence of △-Y exchanges and/or vertex expansions. In the present paper, we show that the removal of any vertex of J and all edges incident to that vertex produces an intrinsically linked graph. This result offers more intrinsically knotted graphs which hold for the conjecture presented in Adams＇ book （Adams C. The Knot Book. New York： W. H. Freeman and Company, 1994）, that is, the removal of any vertex from an intrinsically knotted graph yields an intrinsically linked graph.Let G be a complete p-partite graph with 2 edges removed, p ≥ 7, which is intrinsically knotted. Let J represent any graph obtained from G by a finite sequence of △-Y exchanges and/or vertex expansions. In the present paper, we show that the removal of any vertex of J and all edges incident to that vertex produces an intrinsically linked graph. This result offers more intrinsically knotted graphs which hold for the conjecture presented in Adams＇ book （Adams C. The Knot Book. New York： W. H. Freeman and Company, 1994）, that is, the removal of any vertex from an intrinsically knotted graph yields an intrinsically linked graph.

关 键 词：intrinsically knotted graph △-Y exchange vertex-expansion 

分 类 号：O157.5[理学—数学]