The Journal of the Indian Mathematical Society

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New Proof of 4-Colourability of a Class of Graphs


     

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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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  • New Proof of 4-Colourability of a Class of Graphs

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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).