(a) Show that every tree on n vertices has exactly two 2-colorings.

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In this question all graphs are simple and n is an arbitrary positive integer.
Transcribed Image Text:In this question all graphs are simple and n is an arbitrary positive integer.
(a) Show that every tree on n vertices has exactly two 2-colorings.
(b) Show that if a 2-colorable graph G has exactly two 2-colorings, then any two cycles
contained in G (i.e., as subgraphs) must have a vertex in common.
Transcribed Image Text:(a) Show that every tree on n vertices has exactly two 2-colorings. (b) Show that if a 2-colorable graph G has exactly two 2-colorings, then any two cycles contained in G (i.e., as subgraphs) must have a vertex in common.
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