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29 March 2024
 
  » arxiv » math.CO/0308105

 Article overview


A note on potentially $K_4-e$ graphical sequences
Chunhui Lai ;
Date 12 Aug 2003
Journal Australasian Journal of Combinatorics, 24(2001), 123-127
Subject Combinatorics MSC-class: 05C07; 05C35 | math.CO
AbstractA sequence $S$ is potentially $K_4-e$ graphical if it has a realization containing a $K_4-e$ as a subgraph. Let $sigma(K_4-e, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $sigma(S)geq sigma(K_4-e, n)$ is potentially $K_4-e$ graphical. Gould, Jacobson, Lehel raised the problem of determining the value of $sigma (K_4-e, n)$. In this paper, we prove that $sigma (K_4-e, n)=2[(3n-1)/2]$ for $ngeq 7$, and $n=4,5,$ and $sigma(K_4-e, 6)= 20$.
Source arXiv, math.CO/0308105
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