Abstract
Colouring graphs is one of the oldest problems of graph theory. As it is a kind of labelling, colouring has always been one of the main study areas in graph theory and related fields, especially when combinatorial calculations are needed. The most well-known and cited result on colouring is the Birkhoff–Lewis Theorem. It gives a step-by-step reduction method to calculate the chromatic polynomial of any given graph as the difference of the chromatic polynomials of two smaller graphs, one is edge deleted and the other is edge contracted. Here, we give some short-cut results which enables us to calculate the chromatic polynomial of a relatively large graph by dividing it into smaller graphs.
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© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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Sanli, U., Paikray, S.K., Cangul, I.N. (2021). New Results on Chromatic Polynomials. In: Paikray, S.K., Dutta, H., Mordeson, J.N. (eds) New Trends in Applied Analysis and Computational Mathematics. Advances in Intelligent Systems and Computing, vol 1356. Springer, Singapore. https://doi.org/10.1007/978-981-16-1402-6_8
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DOI: https://doi.org/10.1007/978-981-16-1402-6_8
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