| SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS |
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| 引用本文： | WANG Zhijian Department of Mathematics,Suzhou Railway Teachers College,Suzhou 215009,China. SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS[J]. 系统科学与复杂性, 1993, 0(3) |
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| 作者姓名： | WANG Zhijian Department of Mathematics Suzhou Railway Teachers College Suzhou 215009 China |
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| 作者单位： | WANG Zhijian Department of Mathematics，Suzhou Railway Teachers College，Suzhou 215009，China |
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| 摘 要： | Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x(G), x_1(G) and x_2(G), respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:(i)|2p~(1/2)|-ε_1≤x(G)+x_1(G)≤2p-2 and 0≤x(G)·x_1(G)≤(p-1)~2 for p≥2,(ii)|2p~(1/2)|+ε_1≤x(G)+x_2(G)≤2p-1 and 0≤x(G)·x_2(G)≤p(p-1) for p≥3,(iii)p≤x_1(G)+x_2(G)≤2p-1 and 0≤x_1(G)·x_2(G)≤p(p-1) for p≥3,where ε_1=0, if p~(1/2) is an odd integer, 1, otherwise,ε_2=1, if p~(1/2) is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.
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SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS |
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| WANG Zhijian. SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS[J]. Journal of Systems Science and Complexity, 1993, 0(3) |
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| Authors: | WANG Zhijian |
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| Affiliation: | WANG Zhijian Department of Mathematics,Suzhou Railway Teachers College,Suzhou 215009,China |
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| Abstract: | |
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| Keywords: | Complementary graph chromatic number edge chromatic number total chromatic number theorem of Nordhaus-Gaddum class |
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