The game chromatic number and game coloring number of trees and caterpillars
碩士 === 國立中山大學 === 應用數學系 === 87 === In this thesis, we consider the game chromatic number and game coloring number for trees and caterpillars. It is known that the game coloring number of a tree is at most 4 and there exist trees with game coloring number 4. We show t...
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| Format: | Others |
| Language: | en_US |
| Published: |
1999
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| Online Access: | http://ndltd.ncl.edu.tw/handle/67904787560440113483 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系 === 87 === In this thesis, we consider the game chromatic number and game coloring number for trees and caterpillars.
It is known that the game coloring number of a tree is at most 4 and there exist trees with game coloring number 4.
We show the following:
(1)10 is the minimum number of vertices for a tree (or caterpillar) with game coloring number 4.
(2)14 is the minimum number of vertices for a tree (or caterpillar) with game chromatic number 4.
(3)T is a 3-regular caterpillar and |V(T)| not less than 102, then $\chi_g(T) = 4$.
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