Outerplanar graph with an uncooperative partner
碩士 === 國立屏東教育大學 === 應用數學系 === 96 === The game chromatic number of a graph is introduced by Bodlaender in [1], where the game chromatic number of a tree is discussed, and it is conjectured that the game chromatic number of a planar graph is bounded. It is known that there are outerplanar graphs G wit...
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| Format: | Others |
| Language: | en_US |
| Online Access: | http://ndltd.ncl.edu.tw/handle/51683434160067657942 |
| Summary: | 碩士 === 國立屏東教育大學 === 應用數學系 === 96 === The game chromatic number of a graph is introduced by Bodlaender in [1], where the game chromatic number of a tree is discussed, and it is conjectured that the game chromatic number of a planar graph is bounded.
It is known that there are outerplanar graphs G with χg(G) = 6. It is also known that every outerplanar graph G has χg(G) at most 7. The question is whether or not there is an outer planar graph G with χg(G) = 7.
In this paper, we construct an outerplanar graph with game chromatic number 6 and analyse its structures and properties.
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