1. Tight product and semi-coloring of graphs Masaru Kamada Tokyo University of Science Graph Theory Conference in honor of Yoshimi Egawa on the occasion his 60 th birthday September 10-14, 2013

2. In this talk, all graphs are finite, undirected and allowed multiple edges without loops. No loops Multiple edges

4. Example

5. The main result

6. Almost regular graph

8. Outline of proof of Lemma 2

12. Outline of proof of Lemma 3

17. Example of case II

18. Example of subcase II-ii

24. Tight product

25. Example 25

26. Example 26

27. The existence of the tight product (1)

29. The existence of the tight product (2)

31. Thank you for your attention

32. Proper-edge-coloring

33. Classification of simple graphs

34. Example Class-1Class-2 1 1 3 2 3 2 1 5 4 5 33 1 2 4 2