Tight product and semi coloring of graphs
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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.

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Tight product and semi coloring of graphs

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 60th birthday

September 10-14, 2013


Multiple edges

No loops


Example
Example multiple edges without loops.


The m ain result
The m multiple edges without loops.ain result


A lmost regular graph
A multiple edges without loops.lmost regular graph


O utline of proof of lemma 2
O multiple edges without loops.utline of proof of Lemma 2


Outline of proof of lemma 3
Outline of proof of Lemma 3 multiple edges without loops.


Example of case II multiple edges without loops.


Example of subcase II-ii multiple edges without loops.


Tight product
Tight product multiple edges without loops.


Example1
Example multiple edges without loops.

25


Example2
Example multiple edges without loops.

26


The existence of the tight product 1
The existence of the tight product multiple edges without loops.(1)


The existence of the tight product 2
The existence of the tight product (2) multiple edges without loops.


Thank you for your attention
Thank you for your attention multiple edges without loops.


P roper edge coloring
P multiple edges without loops.roper-edge-coloring


Classification of simple graphs
Classification of simple graphs multiple edges without loops.


Example3
Example multiple edges without loops.

Class-1

Class-2

2

5

4

1

1

3

2

4

5

1

3

3

3

1

2

2


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