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国家自然科学基金(61070230)

作品数:9 被引量:18H指数:2
相关作者:张欣刘桂真吴建良于永滕聪更多>>
相关机构:山东大学山东经济学院兰州大学更多>>
发文基金:国家自然科学基金国家教育部博士点基金更多>>
相关领域:理学自动化与计算机技术电子电信生物学更多>>

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切换到高一层路网最近四个点的最短路算法
2010年
针对基于大规模图的最短路问题求解速度慢的问题,提出了一个基于路网等级的求最短路的快速近似算法。该算法首先求出高一层路网到起点的4个最近点和到终点的4个最近点及最短路径,由高一层路网形成的子图T再加上这8个最短路径形成图T′,在T′上求起点到终点的最短路。这种设计使得该算法适合在超大规模图上求解,理论上也证明了精度可控,同时预处理数据也是可行的,从而使两点间最短路的求解速度大大提高。在纽约公路网上的测试结果说明了该算法的有效性和合理性。
滕聪
关键词:最短路问题DIJKSTRA算法时间复杂度
On Edge Colorings of 1-Toroidal Graphs被引量:2
2013年
A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree △ ≥ 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree △ for each A ≤ 8.
Xin ZHANGGui Zhen LIU
Group Edge Choosability of Planar Graphs without Adjacent Short Cycles被引量:1
2013年
In this paper, we prove that 2-degenerate graphs and some planar graphs without adjacent short cycles are group (△ (G)+1)-edge-choosable, and some planar graphs with large girth and maximum degree are group △(G)-edge-choosable.
Xin ZHANGGui Zhen LIU
关键词:GIRTH
关于可嵌入曲面图的列表(d,1)-全标号问题(英文)被引量:1
2011年
图的(d,1)-全标号问题最初是由Havet等人提出的.在本文中,我们考虑了可嵌入曲面图的列表(d,1)-全标号问题,并证明了其列表(d,1)-全标号数不超过△(G)+2d.
于永张欣刘桂真
关键词:(D,1)-全标号
1-平面图的线性荫度(英文)被引量:8
2011年
证明了最大度△≥33的1-平面图的线性荫度为[△/2]
张欣刘桂真吴建良
关键词:线性荫度
完全图中的正常染色的路和圈(英文)
2011年
令K_n^c表示n个顶点的边染色完全图.令△^(mon)(K_n^c)表示K_n^c的顶点上关联的同种颜色的边的最大数目.如果K_n^c中的一个圈(路)上相邻的边染不同颜色,则称它为正常染色的.B.Bollobas和P.Erd(o|¨)s(1976)提出了如下猜想:若△^(mon)(K_n^c)<[n/2],则K_n^c中含有一个正常染色的Hamilton圈.这个猜想至今还未被证明.我们研究了上述条件下的正常染色的路和圈.
王光辉周珊
关键词:完全图
Light Subgraphs in the Family of 1-Planar Graphs with High Minimum Degree被引量:2
2012年
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, it is shown that each 1-planar graph with minimum degree 7 contains a copy of K2 V (K1 ∪ K2) with all vertices of degree at most 12. In addition, we also prove the existence of a graph K1 V (K1∪K2) with relatively small degree vertices in 1-planar graphs with minimum degree at least 6.
Xin ZHANGGui Zhen LIUJian Liang WU
关键词:LIGHTNESSHEIGHTDISCHARGING
New Upper Bounds on Linear Coloring of Planar Graphs被引量:1
2012年
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, it is proved that every planar graph G with girth g and maximum degree A has (1) lc(G) ≤ △ + 21 if △ ≥ 9; (2) lc(G) ≤[△/2]+ 7 if g≥5; (3) lc(G) ≤ [△/2]+2ifg≥7and△ ≥7.
Bin LIUGui Zhen LIU
关键词:GIRTH
Properties of Hamilton cycles of circuit graphs of matroids被引量:5
2013年
Let G be a circuit graph of a connected matroid. P. Li and G. Liu [Comput. Math. Appl., 2008, 55: 654-659] proved that G has a Hamilton cycle including e and another Hamilton cycle excluding e for any edge e of G if G has at least four vertices. This paper proves that G has a Hamilton cycle including e and excluding e' for any two edges e and e' of G if G has at least five vertices. This result is best possible in some sense. An open problem is proposed in the end of this paper.
Hao FAN Guizhen LIU
关键词:MATROID
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