关于蕴含P_k可图序列的ERDS-JACOBSON-LEHEL猜想

An Erds Jacobson Lehel Conjecture About Potentially P k Graphic Sequences

设σ（ｋ，ｎ）是具有下述性质的最小正偶数，每个度和至少为σ（ｋ，ｎ）且没有零项的ｎ项可图序列都是蕴含Ｐｋ可图的．本文给出了当ｋ５，２ｋ＋２ｎ５ｋ－１２时，σ（ｋ，ｎ）的一个下界，并确定了ｋ＝５，６，７时，σ（ｋ，ｎ）的值，即证明了Ｅｒｄｏｓ－Ｊａｃｏｂｓｏｎ－Ｌｅｈｅｌ关于σ（ｋ，ｎ）的猜想对ｋ＝５且ｎ１３，ｋ＝６且ｎ１５，以及ｋ＝７且ｎ１７时成立．

Let σ(k,n) be the smallest positive even number such that every graphic sequence π without zero term, if σ(π)σ(k,n), then π is potentially P k graphic. We give a lower bound for σ(k,n) , where k5,2k+2n5k-12] , and determine the value of σ(k,n) ,for k=5,6,7 , proving that Erds Jacobson Lehel conjecture is true for k=5 and n13, k=6 and n15,k=7 and n17 .