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[PDF] The Thickness and Chromatic Number of r - Gammeter.com

[PDF] The Thickness and Chromatic Number of r - Gammeter.com

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37<br />

25<br />

31 2043 8 7 441932<br />

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29 18 41 6 5 42 17 30<br />

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43 32 7 2019 8 3144<br />

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41 30 5 18 17 6 29 42<br />

40<br />

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14 13<br />

Figure 7: Second two layers <strong>of</strong> a thickness-4 de<strong>com</strong>position <strong>of</strong> I[4].<br />

Many <strong>of</strong> the ideas that were used in showing that the r-inflated icosahedral graph<br />

has thickness exactly r can be used to show that the thickness <strong>of</strong> the r-inflation <strong>of</strong><br />

any tree is at most ⌈ r ⌉. This will be ac<strong>com</strong>plished in the next subsection.<br />

2<br />

15<br />

26<br />

38<br />

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2

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