Note: Degree sequences and graphs with disjoint spanning trees

Authors:
Hong-Jian Lai;Yanting Liang;Ping Li;Jinquan Xu
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China and Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, HuiZhou University, HuiZhou, Guangdong 561007, China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

The design of an n processor network with a given number of connections from each processor and with a desirable strength of the network can be modeled as a degree sequence realization problem with certain desirable graphical properties. A nonincreasing sequence d=(d"1,d"2,...,d"n) is graphic if there is a simple graph G with degree sequence d. In this paper, it is proved that for a positive integer k, a graphic sequence d has a simple realization G which has k edge-disjoint spanning trees if and only if either both n=1 and d"1=0, or n=2 and both d"n=k and @?"i"="1^nd"i=2k(n-1).