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Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
-
Shishuo Fu
and
James A. Sellers
Published/Copyright:
October 2, 2012
Abstract.
Recently, Gu, Lai and Liang proved necessary and sufficient conditions for a given sequence of positive integers 
to be the degree sequence of a line-Hamiltonian multigraph. Our goal in this note is to utilize this result to prove a closed formula for the function 
, the number of degree sequences with degree sum 
representable by line-Hamiltonian multigraphs. Indeed, we give a truly elementary proof that
where 
is the number of unrestricted integer partitions of j.
Received: 2011-05-03
Revised: 2011-12-10
Accepted: 2012-03-04
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Two-Color Babylon
- On Abelian and Additive Complexity in Infinite Words
- Approximations of Additive Squares in Infinite Words
- The Googol-th Bit of the Erdős–Borwein Constant
- Odd Repdigits to Small Bases Are Not Perfect
- Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
- The Characteristic Sequence and p-Orderings of the Set of d-th Powers of Integers
- Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
- Sum-Products Estimates with Several Sets and Applications
- The 2-Adic, Binary and Decimal Periods of 1/3k Approach Full Complexity for Increasing k
- A Proof of Catalan's Convolution Formula
- Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
- The Impossibility of Certain Types of Carmichael Numbers
- Integer Subsets with High Volume and Low Perimeter
- Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
- A Generalized Diagonal Wythoff Nim
- A Recursive Process Related to a Partizan Variation of Wythoff
- The (r1,...,rp)-Stirling Numbers of the Second Kind
- Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
- On k-Lehmer Numbers
