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Prove the chromatic number of any tree is two. Recall, a tree is a connected graph with no cycles. (a) Describe a procedure to color the tree below. /attached picture/ (b) The chromatic number of Cn is two when n is even. What goes wrong when n is odd? (c) Prove that your procedure from part (a) always works for any tree.

Prove the chromatic number of any tree is two. Recall, a tree is a connected graph with no cycles. (a) Describe a procedure to color the tree below. /attached picture/ (b) The chromatic number of Cn is two when n is even. What goes wrong when n is odd? (c) Prove that your procedure from part (a) always works for any tree.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Discrete Maths Oscar Levin 3rd eddition 4.4.6:

Prove the chromatic number of any tree is two. Recall, a tree is a
connected graph with no cycles.

(a) Describe a procedure to color the tree below.

/attached picture/

(b) The chromatic number of Cn is two when n is even. What goes
wrong when n is odd?

(c) Prove that your procedure from part (a) always works for any
tree.

(d) Now, prove using induction that every tree has chromatic num-
ber 2.

ps: I'd be so glad if you include every detail of the solution. & Thank you soooo much. You are doing a great job!

Prove the chromatic number of any tree is two. Recall, a tree is a connected graph with no cycles. 6. (a) Describe a procedure to color the tree below. 4.4. COLORING 275 (b) The chromatic number of C, is two when n is even. What goes wrong when n is odd? (c) Prove that your procedure from part (a) always works for any tree. (d) Now, prove using induction that every tree has chromatic num- ber 2.
Transcribed Image Text:Prove the chromatic number of any tree is two. Recall, a tree is a connected graph with no cycles. 6. (a) Describe a procedure to color the tree below. 4.4. COLORING 275 (b) The chromatic number of C, is two when n is even. What goes wrong when n is odd? (c) Prove that your procedure from part (a) always works for any tree. (d) Now, prove using induction that every tree has chromatic num- ber 2.
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