(A_(n);B_(n))同奇偶m-可图的充分条件  

A sufficient condition for(A_(n);B_(n)) to be identical parity m-graphic

作　　者：郭纪云 李海燕 郭锦 蔡白光 GUO Ji-yun;LI Hai-yan;GUO Jin;CAI Bai-guang(Center for Applied Mathematics,Tianjin University,Tianjin 300072,China;School of Science,Hainan University,Haikou 570228,Hainan,Chian)

机构地区：[1]天津大学应用数学中心,天津300072 [2]海南大学理学院,海南海口570228

出　　处：《山东大学学报（理学版）》2022年第3期85-88,共4页Journal of Shandong University(Natural Science)

基　　金：国家重点研发计划资助项目(2018YFA0704701);国家自然科学基金资助项目(11921001,11601108);海南省自然科学基金资助项目(121MS001)。

摘　　要：设A_(n)={a_(1),a_(2),…,a_(n)}和B_(n)={b_(1),b_(2),…,b_(n)}是2个非增非负整数序列,其中a_(i)≤b_(i)(i=1,2,…,n)。若A_(n)及B_(n)满足a_(1)≥a_(2)≥…≥a_(n)且a_(i)=a_(i)+1蕴含b_(i)≥b_(i)+1(i=1,2,…,n-1),则称A_(n)和B_(n)遵从良序。若对于每一个i=1,…,n,都有a_(i)≡b_(i)(mod 2)且存在n阶m-图G,使得a_(i)≤d_(G)(vi)≤b_(i)及d_(G)(vi)≡b_(i)(mod 2),则称序列对(A_(n);B_(n))是同奇偶m-可图的,并称G为其一个实现。给出(A_(n);B_(n))同奇偶m-可图的一个充分条件,其中A_(n)和B_(n)遵从良序。Let A_(n)={a_(1),a_(2),…,a_(n)}and B_(n)={b_(1),b_(1),…,b_(n)}be two sequences of nonnegative integers with a_(i)≤b_(i)for i=1,2,…,n.If A_(n)and B_(n)satisfy a_(1)≥a_(2)≥…≥a_(n)and a_(i)=a_(i)+1 implies b_(i)≥b_(i)+1 for i=1,2,…,n-1,then A_(n)and B_(n)are sa_(i)d to be in good order.If a_(i)≡b_(i)(mod 2)for each i and there exists a m-graph G with vertices v1,…,vn such that a_(i)≤d_(G)(vi)≤b_(i)and d_(G)(vi)≡b_(i)(mod 2)for each i,then(A_(n);B_(n))is sa_(i)d to be identical parity m-graphic,G is called a realization of the pa_(i)r.A constructive method is performed to prove a sufficient condition for(A_(n);B_(n))to be identical parity m-graphic,where A_(n)and B_(n)are in good order.

关 键 词：度序列 构造性方法 同奇偶m-可图 

分 类 号：O157.5[理学—数学]