# h1 - 3 Let G be a graph with δ G ≥ 2 Prove that G has a...

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MATH 4171 Graph Theory SPRING 2006 Homework Set I (Four problems) Due date : Monday 1-30-06 1. Describe a real world problem (preferable from your own ﬁeld) that can be modeled by graphs. Specify vertices, edges, and the incidence relation for your graph. 2. Is there a simple graph on 2006 vertices for which no two vertices have the same degree? You need to justify your conclusion.
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Unformatted text preview: 3. Let G be a graph with δ ( G ) ≥ 2. Prove that G has a subgraph which is a cycle. 4. Prove that there exists a graph (could have loops and multiple edges) with degrees d 1 , d 2 , ..., d n if and only if d 1 + d 2 + ... + d n is even. Important —– No Late Homework Will be Accepted —–...
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## This note was uploaded on 02/17/2009 for the course MATH 4171 taught by Professor Lax,r during the Spring '08 term at LSU.

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