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图的染色与标号
  • 项目名称：图的染色与标号
  • 项目类别：面上项目
  • 批准号：10771197
  • 申请代码：A011602
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2010-12-31
  • 项目负责人：王维凡
  • 负责人职称：教授
  • 依托单位：浙江师范大学
  • 批准年度：2007
中文摘要：

图的染色与标号是图论研究的重要内容,在现代计算机科学、信息科学、管理科学等领域有着十分广泛的应用，近些年来得到了国内外同行的极大关注。本项目研究图的各种染色与标号问题，如无圈染色、injective 染色、L(p,q)-标号、(k,1)-全标号等。围绕著名的J.R.Griggs 和 R.K.Yeh 猜想展开对图的L(2,1)-标号的重点研究，扩展满足该猜想的图类. 研究平面图的平方色数，以证明 G.Wegner 猜想为终极目标.推广已知的全染色结果到(2,1)-全标号的情形,力图解决或部分解决该领域的F.Havet 和 M.L.Yu 猜想.给出平面图、高维曲面图、chordal 图等图类的Injective 色数的好的上界，刻画外平面图、格子图、大围长平面图等的 injective 色数。拟在三年内完成学术论文至少15篇。

中文主题词： 图;染色;标号;频道设计
结论摘要：

英文主题词Graph;Coloring;Labelling;Frequency channel assigment

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 67
  • 0
  • 0
  • 0
  • 0
期刊论文
Adjacent verte distinguishing edge-colorings of graphs with smaller maximum average degree
A note on full orientation of a graph
The surviving rate of a graph for the firefighter problem
Planar graphs withou 4-cycles are acyclically 6-choosable
Some results on distance two labelling of outerplanar graphs
Independent sets in direct product of vertex-transitive graphs
Adjacent vertex distinguishing total colorings of $K_4$-minor free graphs
Linear coloring of planar graphs with large girth
Star coloring of sparse graphs
Adjacent vertex distinguishing total colorings of outerplanar graphs
Choosability of toroidal graphs without short cycles
On 3-colorability of planar graphs without adjacent short cycles
k-fold coloring of planar graphs
Some results about modified Zagreb indices
PI indices for some classes of bicyclic graphs
The modified Zagreb indices about disjunction and symmetric difference of graphs
The modified Zagreb indices about join and composition of graphs
Some graphs with extremal PI index
The surviving rate of an infected network
On (d,1)-total numbers of graphs
Injective chromatic number of planar graphs
A sufficient condition for a planar graph to be Class 1
(2,1)-Total labelling of trees with sparse vertices of maximu degree
On the 9 total colorability of planar graphs with maximum degree 8 and without intersecting triangle
(2,1)-Total number of trees with maximum degree three
On the 3-colorability of planar graphs without 4-, 7- and 9-cycles
The edge-face coloring of graphs embedded in a surface of characteristic zero
Equitable list coloring of planar graphs without 4- and 6-cycles
Enumeration of uniquely pancyclic digraphs with the least arcs
Two kinds of hook length formulas for complete m-ary trees,
Hao Jianxiu, PI index of some simple pericondensed hexagonal systems,
Hao Jianxiu, The PI index of gated amalgam
L(2,1)-labelling number of 2-outer planar graphs
An upper bound for the adjacent vertex-distinguishing chromatic number of a graph
Some bounds for PI indices,
Adjacent vertex distinguishing total coloring of graphs with lower average degree
Diameters of uniform subset graphs
Acyclic 5-choosability of planar graphs without 4-cycles
On 3-colorable planar graphs without short cycles
Coupled choosability of plane graphs
Note on coloring the square of an outerplanar graph
The linear $2$-arboricity of $K4$-minor-free graphs
The numbers of spanning trees in some graphs
The vertex-arboricity of planar graphs
Improper choosability of graphs of nonnegative characteristic
Edge choosability of planar graphs without 5-cycles with a chord
Normalized matching property of restricted subspace lattices
Nested chain order
Equitable list colorings of planar graphs without short cycles
Vertex-distinguishing total chromatic number of CmVWn
q-weighted log-concavity and q- product theorem on the normality of posets
Two linear transformations preserving log-concavity
Labelling planar graphs without 4-cycles with a condition on distance two
A relaxation of Havel's 3-color problem
Linear coloring of graphs embeddable in a surface of nonnegative characteristic
图Cm∨Wn的点可区别全色数
Sm×Sn,Sm×Fn和Sm×Wn的点可区别全色数
三正则图的Upper减控制数
一些图的生成树数
关于Cm·Cn,Cm·Sn和Cm·Kn的邻点可区别全色数
围长至少为6的平面图的线性染色
2-连通外平面图的邻点可区别全染色
第一类图的一个充分条件
几类图的符号全控制数
2-外平面图的L（2，1）-标号数
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