邻域并和［a,b］因子

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Abstract:

Let a≤b be integers and G a graph. A spanning subgraph F of G is called an [a,b] factor of G if a≤d_F(v)≤b for all v∈V(G). A sufficient condition concerning neighborhood unions for the existence of an [a,b] factor in a graph is given. The author prove the following result: Let a(a+b)(2a+2b-3)/b. Assume |N_G (u)∪N_G (v)|≥an/(a+b), for each pair of nonadjacent vertices u,v in G and the minimum degree is at least a, Then G has an [a,b] factor.

Key words: Ｇｒａｐｈ, ［a,b］-ｆａｃｔｏｒ, Ｎｅｉｇｈｂｏｒｈｏｏｄｕｎｉｏｎ．

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　０５Ｃ７０

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Su Bentang . Neighborhood Unions and [a,b] Factors[J].Acta mathematica scientia,Series A, 1999, 19(5): 481-485.

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８　ＫａｔｅｒｉｎｉｓＰ．Ｔｏｕｇｈｎｅｓｓｏｆｇｒａｐｈａｎｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｄｅｇｒｅｅｆａｃｔｏｒｓ．ＤｉｓｃｒｅｔｅＭａｔｈ，１９９０，８０：８１－９２
９　阎桂英．k-因子的存在与邻域并条件．纯粹数学与应用数学，１９９４，１０（特刊）：１３５－１４２

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[1]	Liu Jingxin, Wu Hongxia, Zeng Yunbo. On the Ingegrable Coupled Generalization of Dispersionless BKP Hierarchy and Its Solutions [J]. Acta mathematica scientia,Series A, 2017, 37(2): 313-325.
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[3]	WANG Bin. Phase Transition in A Random Graph Process with Preferential Deletion and Limiting on Vertices [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1554-1577.
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[6]	SUN Sheng, WANG Fang-Lei, AN Yu-Kun. Strong Approximations of Linear Processes [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1050-1055.
[7]	ZHANG Liang, YAO Xiao-Hua. Controllability of a Nonlinear Parabolic Equation with Maximal Monotone Graph [J]. Acta mathematica scientia,Series A, 2011, 31(5): 1439-1446.
[8]	LI Zeng-Ti. Lattices Associated with Distance-Regular Graphs I [J]. Acta mathematica scientia,Series A, 2011, 31(2): 492-499.
[9]	YAO Bing, CHENG Hui, YAO Meng, ZHANG Zhong-Fu. Behaviors of Vertex Neighbors of Trees Under Some Graph Colorings [J]. Acta mathematica scientia,Series A, 2011, 31(2): 567-576.
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[14]	DI Chao-Hui, GUO Xiao-Feng. Extending Matchings in Odd Graphs [J]. Acta mathematica scientia,Series A, 2009, 29(2): 365-372.
[15]	Liu Yan；Yang Chunxia. Factor-critical Graph G with \|V(G)\|+2} Maximum Matchings [J]. Acta mathematica scientia,Series A, 2009, 29(2): 486-493.

Neighborhood Unions and [a,b] Factors

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