coloring planar graphs
TRANSCRIPT
Coloring Planar Graphs
UPenn Summer Math Academy, Summer 2018
Ordering the vertices
10
10
10
1010
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
10
10
1010
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
10
1010
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
1010
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
410
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
10
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
10
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
1010
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
810
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
10
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
10 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 10
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
10
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
10
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
10
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
16
10
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
10
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
10
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
10
Ordering the vertices
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 6 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20
Coloring with 5 colors
1
2
3
45
6
7
89
10
11
12 13
14
15
16
17
18
19
20