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Tight product and semi-coloring of graphs. Masaru Kamada Tokyo University of Science Graph Theory Conference i n honor of Yoshimi Egawa on the occasion his 60 th birthday September 10-14, 2013. In this talk, all graphs are finite, undirected and allowed multiple edges without loops. - PowerPoint PPT Presentation
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Tight product and semi-coloring of graphs
Masaru KamadaTokyo University of Science
Graph Theory Conferencein honor of Yoshimi Egawa on the occasion his 60th birthday
September 10-14, 2013
• In this talk, all graphs are finite, undirected and allowed multiple edges without loops.
No loopsMultiple edges
Example
{1}{2 }{3 }{1,2}{1,3 }{2,3 }
The main result
Almost regular graph
Outline of proof of Lemma 2
Outline of proof of Lemma 3
Example of case II
Example of subcase II-ii
{1}{2 }{3 }{1,2}{2,3 }
{1}{2 }{3 }{1,2}{2,3 }
{1}{2 }{3 }{1,2}{2,3 }
Tight product
Example
25
Example
26
The existence of the tight product (1)
The existence of the tight product (2)
Thank you for your attention
Proper-edge-coloring
Classification of simple graphs
Example
Class-1 Class-2
1
1
32
3
2
15
4
5 3 3 1
2
42
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