Open AccessInvalid Counterexample in Graph Theory
Author(s) -
Qin Yu
Publication year - 2010
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v2n4p130
Subject(s) - counterexample , mathematics , graph , combinatorics , property (philosophy) , discrete mathematics , epistemology , philosophy
By using the color exchange method and convertible property of the topological graph for inside cycle and outside, the colors of the vertexes on the two cycles in the same position can be corresponded with each other. Thus prove the reducibility of the 3-cycle and 4-cycle with both vertexes inside and outside. Meanwhile, point out the invalid counterexample of the “Heawood graph” which was commonly accepted in many textbooks