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order; degree-continuous graph; degree set; Erdös-Gallai theorem; regular graph
The minimum orders of degree-continuous graphs with prescribed degree sets were investigated by Gimbel and Zhang, Czechoslovak Math. J. 51 (126) (2001), 163–171. The minimum orders were not completely determined in some cases. In this note, the exact values of the minimum orders for these cases are obtained by giving improved upper bounds.
[1] S. A.  Choudum: A simple proof of the Erdös-Gallai theorem on graph sequences. Bull. Austral. Math. Soc. 33 (1986), 67–70. DOI 10.1017/S0004972700002872 | MR 0823853
[2] P.  Erdös, T.  Gallai: Graphs with prescribed degrees of vertices. Mat. Lapok 11 (1960), 264–274. (Hungarian)
[3] J.  Gimbel, P.  Zhang: Degree-continuous graphs. Czechoslovak Math.  J. 51 (126) (2001), 163–171. DOI 10.1023/A:1013718124383 | MR 1814641
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