If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodi...If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.展开更多
设G是一个简单图,i是一个正整数.X是V(G)的一个子集.如果X中任意两个点的距离都大于i,则称X是一个i-宽度箱.i叫做X的宽度.一个图G的泛宽度色数χρ(G)是使得G的顶点集V(G)被剖分成宽度两两不同的k个宽度箱的最小整数k.本文给出了轮,扇及...设G是一个简单图,i是一个正整数.X是V(G)的一个子集.如果X中任意两个点的距离都大于i,则称X是一个i-宽度箱.i叫做X的宽度.一个图G的泛宽度色数χρ(G)是使得G的顶点集V(G)被剖分成宽度两两不同的k个宽度箱的最小整数k.本文给出了轮,扇及图Kn的推广的haj s sum的泛宽度色数.展开更多
Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show th...Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show that to prove Hajos' conjecture,it is sufficent to prove this new conjecture for 3-connected graphs.Furthermore,a special 3-cut is considered also.展开更多
文摘If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.
基金This research is partially supported by the National Postdoctoral Fund of China and Natural Science Foundation of China(No. 10001035) This work was finished while the author was working for Academy of Mathematics and Systems Science, Chinese of Academy
文摘Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos' conjecture.and show that to prove Hajos' conjecture,it is sufficent to prove this new conjecture for 3-connected graphs.Furthermore,a special 3-cut is considered also.
