# A Characterization of Box-bounded Degree Sequences of Graphs

A Characterization of Box-bounded Degree Sequences of Graphs Let $$A_n=(a_1,a_2,\ldots ,a_n)$$ A n = ( a 1 , a 2 , … , a n ) and $$B_n=(b_1,b_2,\ldots ,b_n)$$ B n = ( b 1 , b 2 , … , b n ) be nonnegative integer sequences with $$A_n\le B_n$$ A n ≤ B n and $$b_i\ge b_{i+1},a_i+b_i\ge a_{i+1}+b_{i+1}, i=1,2\ldots , n-1$$ b i ≥ b i + 1 , a i + b i ≥ a i + 1 + b i + 1 , i = 1 , 2 … , n - 1 . The purpose of this note is to give a good characterization for $$A_n$$ A n and $$B_n$$ B n such that every integer sequence $$\pi =(d_1,d_2,\ldots d_n)$$ π = ( d 1 , d 2 , … d n ) with even sum and $$A_n\le \pi \le B_n$$ A n ≤ π ≤ B n is graphic. This improves related results of Guo and Yin and generalizes the Erdős–Gallai theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

# A Characterization of Box-bounded Degree Sequences of Graphs

, Volume 34 (4) – May 28, 2018
8 pages

/lp/springer_journal/a-characterization-of-box-bounded-degree-sequences-of-graphs-1T8ihtbxR2
Publisher
Springer Japan
Subject
Mathematics; Combinatorics; Engineering Design
ISSN
0911-0119
eISSN
1435-5914
D.O.I.
10.1007/s00373-018-1897-5
Publisher site
See Article on Publisher Site

### Abstract

Let $$A_n=(a_1,a_2,\ldots ,a_n)$$ A n = ( a 1 , a 2 , … , a n ) and $$B_n=(b_1,b_2,\ldots ,b_n)$$ B n = ( b 1 , b 2 , … , b n ) be nonnegative integer sequences with $$A_n\le B_n$$ A n ≤ B n and $$b_i\ge b_{i+1},a_i+b_i\ge a_{i+1}+b_{i+1}, i=1,2\ldots , n-1$$ b i ≥ b i + 1 , a i + b i ≥ a i + 1 + b i + 1 , i = 1 , 2 … , n - 1 . The purpose of this note is to give a good characterization for $$A_n$$ A n and $$B_n$$ B n such that every integer sequence $$\pi =(d_1,d_2,\ldots d_n)$$ π = ( d 1 , d 2 , … d n ) with even sum and $$A_n\le \pi \le B_n$$ A n ≤ π ≤ B n is graphic. This improves related results of Guo and Yin and generalizes the Erdős–Gallai theorem.

### Journal

Graphs and CombinatoricsSpringer Journals

Published: May 28, 2018

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