A note on degree-continuous graphs. (English) Zbl 1174.05038
Summary: The minimum orders of degree-continuous graphs with prescribed degree sets were investigated by J.Gimbel and P.Zhang [Czech.Math.J.51, 163–171 (2001; Zbl 1079.05504)]. 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.
MSC:
| 05C12 | Distance in graphs |
Citations:
Zbl 1079.05504References:
| [1] | S. A. Choudum: A simple proof of the Erdös-Gallai theorem on graph sequences. Bull. Austral. Math. Soc. 33 (1986), 67–70. · Zbl 0571.05048 · doi:10.1017/S0004972700002872 |
| [2] | P. Erdös, T. Gallai: Graphs with prescribed degrees of vertices. Mat. Lapok 11 (1960), 264–274. (In Hungarian.) · Zbl 0103.39701 |
| [3] | J. Gimbel, P. Zhang: Degree-continuous graphs. Czechoslovak Math. J. 51(126) (2001), 163–171. · Zbl 1079.05504 · doi:10.1023/A:1013718124383 |
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