Degree sequences with repeated values
Guantao Chen, Joan P. Hutchinson, Wiktor Piotrowski, Warren E. Shreve, Bing Wei · 2001
A given nonincreasing sequence D = (d1 , d2 , , dn ) is said to contain a (nonincreasing) repetition sequence D # = (d i 1 , d i 2 , , d i k ) for some k # n - 2 if all values of D-D # are distinct and for any d i l # D # there exists some d t # D-D # such that d i l = d t . For any pair of integers n and k with n # k + 2, we investigate the existence of a graphic sequence which contains a given repetition sequence. Our main theorem contains the known results for the special case d i 1 = d i k if k = 1 or k = 2 (see [1, 5, 2]).