平面图的变换与着色的性质
Moves and Coloring Properties for Planar Graph
DOI: 10.12677/AAM.2021.105160, PDF,    国家自然科学基金支持
作者: 韩友发, 刘 佳, 孔令天：辽宁师范大学数学学院，辽宁 大连；阎昕明：广东第二师范学院数学系，广东 广州
关键词: 图着色；双色多项式；图变换；纽结；Graph Coloring； Dichromatic Polynomial； Graph Move； Knot
摘要: 本文研究了平面图着色的性质，给出了平面图的变换，包括树形变换、三角形变换(n-圈变换)和桥变换等，并且利用图的双色多项式证明了这些变换不改变着色数，进而研究了某些平面图的着色性质。
Abstract: This paper studies the coloring properties of planar graph, gives their moves including tree-move triangle-move (n-circle-move), bridge-move, and proves that these moves don’t change coloring number by using dichromatic polynomial. Furthermore, the coloration of some planar graphs is studied.
文章引用：韩友发, 刘佳, 孔令天, 阎昕明. 平面图的变换与着色的性质[J]. 应用数学进展, 2021, 10(5): 1508-1514. https://doi.org/10.12677/AAM.2021.105160

参考文献

[1] Alexander, J.W. (1928) Topological Invariants of Knots and Links. Transactions of the American Mathematical Society, 30, 275-306. [Google Scholar] [CrossRef] 
[2] Conway, J.H. (1970) An Enumeration of Knots and Links, and Some of Their Algebraic Properties. Computational Problems in Abstract Algebra, New York, 29 August-2 September 1970, 329-358. [Google Scholar] [CrossRef] 
[3] Jones, V.F.R. (1989) On Knot Invariants Related to Some Statistical Mechanical Models. Pacific Journal of Mathematics, 137, 311-334. [Google Scholar] [CrossRef] 
[4] Kauffman, L.H. (1988) New Invariants in the Theory of Knots. The American Mathematical Monthly, 95, 195-242. [Google Scholar] [CrossRef] 
[5] Wu, F.Y. (1992) Knot Theory and Statistical Mechanics. Modern Physics, 64, 1099-1131. [Google Scholar] [CrossRef] 
[6] Sumners, D.W. (1990) Untangling DNA. The Mathematical Intelligencer, 12, 71-80. [Google Scholar] [CrossRef] 
[7] Adams, C.C. (2004) The Knot Book. W. H. Freeman and Company, New York.
[8] 韩友发, 亢云凤, 董婷. 平面图的多项式与着色[J]. 辽宁师范大学学报, 2017, 40(3): 289-292.

为你推荐