Dissertation > Excellent graduate degree dissertation topics show

The Fractional Chromtic Numbers of Some Graphs

Author: WangCaiHong
Tutor: LiuXiKui
School: Shandong University of Science and Technology
Course: Applied Mathematics
Keywords: Fractional coloring Fractional chromatic number Product of graphs Sum of graphs Normal of graphs Hypergraph The probabilistic method
CLC: O157.5
Type: Master's thesis
Year: 2008
Downloads: 6
Quote: 0
Read: Download Dissertation

Abstract


The fractional chromatic number of a graph is a variation of the chromatic number.It can provide a better model for some special problems.As an important parameter,the chromatic number of the graph has the values of studying.Firstly,the definition of fractional chromatic number is given in this paper. The fractional chromatic numbers of sum of graphs,normal product of graphs and join of graphs are studied.In terms of the fractional coloring of the vertextransitive graph,the fractional chromatic numbers of circular graphs,powers of cycles and the direct product of theme are studied.Then the upper bound and lower bound of the fractional chromatic numbers of the algorithms of graphs are obtained.What’s more,the relations between the fractional chromatic numbers of the algorithms of graphs and their factors can be perfected.Also,much exacter calculating methods are found.Secondly,the fractional coloring is extended to the finite hypergraph H in this paper.And the properties of the finite hypergraph are given,The fractional chromatic numbers of some special hypergraphs are discussed,such as the odd and even cycles,the linear hypergraph with no cycles,its dual graph,2-section graph, line graph and incidence graph,hypergraph H_q~p(r),r-uniform circular hypergraph and so on.Then the relation between the chromatic number and fractional number of hypergraph is determined.The fractional chromatic numbers of product of hypergraphs and lexicohypergraphic product are discussed.In the last,an upper bound of the fractional chromatic number is given,using the probabilistic method.Form it,an algorithm of calculating the fractional chromatic number is obtained.

Related Dissertations

  1. Colorings of Distance Graphs and Star Extremality of Circulant Graphs,O157.5
  2. The Fractional Chromtic Numbers and Total Fractional Chromtic Numbers of Some Graphs,O157.5
  3. Distance Coloring of Special Classes of Graphs,O157.5
  4. The Research on the Fractional Chromatic Number of Graphs,O157.5
  5. Transversal of Hypergraphs,O157.5
  6. Transversal of Hypergraphs,O157.5
  7. The Packing Coloring and the (p,1) -Total Labelling of Graphs,O157.5
  8. The Spectrum of Linear Hypergraph,O157.5
  9. On [r, s, t]-Coloring of Graph,O157.5
  10. Research on Outlier Data Mining in High Dimensional Space,TP311.13
  11. The Total Coloring, the (Adjacent) Vertex-distinguish Total Coloring and the Fractional Coloring of Graphs,O157.5
  12. (Adjacent) Vertex-distinguishing Total Colorings and Fractional Colorings of Graphs,O157.5
  13. Some Topics on the Coloring Theory of Cycloids,O157.5
  14. Relations among the Parameters of Hypergraphs and Colourings of Hypergraphs,O157.5
  15. The Fractional Chromatic Coloring about Several Kinds of Graphs,O157.5
  16. The Lower Bound on the Size of Edge-Coloring Critical Graph & the Fractional Edge Coloring of Some Graphs,O157.5
  17. Study on Design Theory and Control Method of Permanent Magnet Type Retarder in Automobile,U463.5
  18. Extremal Problems of Intersecting and Sperner Families of Sperner Theory,O157
  19. Research on Extensible Hash Based Dynamic Load Balancing for Parallel Web Crawling,TP391.3
  20. Study on Grid Task Scheduling and Optimization Mechanism,TP393.01

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
© 2012 www.DissertationTopic.Net  Mobile