Meredith graph
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In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973.[1]
The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-Hamiltonian.[2] It has book thickness 3 and queue number 2.[3]
Published in 1973, it provides a counterexample to the Crispin Nash-Williams conjecture that every 4-regular 4-vertex-connected graph is Hamiltonian.[4][5] However, W. T. Tutte showed that all 4-connected planar graphs are hamiltonian.[6]
The characteristic polynomial of the Meredith graph is .
Gallery
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The chromatic number of the Meredith graph is 3.
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The chromatic index of the Meredith graph is 5.
References
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- ↑ Bondy, J. A. and Murty, U. S. R. "Graph Theory". Springer, p. 470, 2007.
- ↑ Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018
- ↑ Script error: No such module "Citation/CS1".
- ↑ Bondy, J. A. and Murty, U. S. R. "Graph Theory with Applications". New York: North Holland, p. 239, 1976.
- ↑ Tutte, W.T., ed., Recent Progress in Combinatorics. Academic Press, New York, 1969.
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