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