New Proof of 4-Colourability of a Class of Graphs
Abstract
The Following result about planar trivalent (homogeneous of degree 3) graphs is well known. [[1], p. 121].
THEOREM A: A planar trivalent graph is face colourable in four colours if and only if it contains a partial graph H, which is homogeneous of degree 2 and has even number of edges in each component of H (A partial graph being a subgraph containing all the vertices).
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Copyright (c) 1974 M. N. Vartak, H. Narayanan
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References
R. G. BUSACKER AND T. L. SAATY, Finite Graphs and Networks, McGraw Hill.
OYSTEIN ORE, The Four Colour Problem, Academic Press.