麦比乌斯梯子C(2n,n)的强边色数

摘要

In this paper,we study the problem of the strong edge-coloring of Mobius ladder C(2n,n). By using the combinatorial method, we obtain the following results: χ ' s(C(2n,n)) = 9 if n=3; χ ' s(C(2n,n))=10 if n=4; χ ' s(C(2n,n))=8 if n=5,8; χ ' s(C(2n,n))=6 if n≥3 and n≡2(mod 4);χ ' s(C(2n,n))=7 if n≥7 and n≡0,1 or 3(mod 4).%本文研究了麦比乌斯梯子 C(2n,n) 的强边染色问题.利用组合分析的方法,得到了如下结果:当n = 3时,χ' s(C(2n,n)) = 9;当n = 4时,χ' s(C(2n,n)) = 10;当n = 5,8时, χ ' s(C(2n,n)) = 8;当n ≥ 3且n ≡ 2(mod 4) 时,χ' s(C(2n,n)) = 6;当n ≥ 7且n ≡ 0,1或3(mod 4)时,χ' s(C(2n,n))=7.