Chvátal Graph
المؤلف:
Bondy, J. A. and Murty, U. S. R
المصدر:
Graph Theory with Applications. New York: North Holland
الجزء والصفحة:
...
24-3-2022
2097
Chvátal Graph
Grünbaum conjectured that for every 
, 
, there exists an 
-regular, 
-chromatic graph of girth at least 
. This result is trivial for 
or 
, but only a small number of other such graphs are known, including the 12-node Chvátal graph, 21-node Brinkmann graph, and 25-node Grünbaum graph. The Chvátal graph is illustrated above in a couple embeddings (e.g., Bondy; Knuth 2008, p. 39).
It has 370 distinct (directed) Hamiltonian cycles, giving a unique generalized LCF notation of order 4 (illustrated above), two of order 6 (illustrated above), and 43 of order 1.
The Chvátal graph is implemented in the Wolfram Language as GraphData["ChvatalGraph"].
The Chvátal graph is a quartic graph on 12 nodes and 24 edges. It has chromatic number 4, and girth 4. The Chvátal graph has graph spectrum 
.
REFERENCES
Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 241, 1976.
Grünbaum, B. "A Problem in Graph Coloring." Amer. Math. Monthly 77, 1088-1092, 1970.
Knuth, D. E. The Art of Computer Programming, Volume 4, Fascicle 0: Introduction to Combinatorial Functions and Boolean Functions.. Upper Saddle River, NJ: Addison-Wesley, 2008.
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