Blocks of a given graph and expansion to a 4-critical graph
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For n∈N, let G be the graph with vertex set {v_0,...,v_3n} defined by v_i↔v_j if and only if |i-j|≤2 and i+j is not divisible by 6.
a) Determine the blocks of G.
b) Prove that adding the edge v_0 v_3n to G creates a 4-critical graph.
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Solution Summary
The blocks of the given graph are stated and graphically displayed. A detailed proof of the fact that adding a specified edge to the given graph yields a graph that is 4-critical is provided.
Education
- AB, Hood College
- PhD, The Catholic University of America
- PhD, The University of Maryland at College Park
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