• Corpus ID: 15876246

On Potentially (K 5 - C 4 )-graphic Sequences.

@article{Hu2007OnP,
  title={On Potentially (K 5 - C 4 )-graphic Sequences.},
  author={Lili Hu and Chunhui Lai},
  journal={Ars Combinatoria},
  year={2007},
  volume={101},
  pages={175-192}
}
In this paper, we characterize the potentially $(K_5-C_4)$-graphic sequences where $K_5-C_4$ is the graph obtained from $K_5$ by removing four edges of a 4 cycle $C_4$. This characterization implies a theorem due to Lai [6]. 
8 Citations
On potentially $K_6-C_5$ graphic sequences
For given a graph $H$, a graphic sequence $\pi=(d_1,d_2,...,d_n)$ is said to be potentially $H$-graphic if there exists a realization of $\pi$ containing $H$ as a subgraph. In this paper, we
A Characterization On Potentially K 6 - C 4 -graphic Sequences.
For given a graph H , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. Let Km − H be the graph obtained
A Characterization On Potentially K2, 5-graphic Sequences
TLDR
This paper characterize potentially $K_{2,5}$-graphic sequences and implies a special case of a theorem due to Yin et al.
On potentially K5-H-graphic sequences
Let Km-H be the graph obtained from Km by removing the edges set E(H) of H where H is a subgraph of Km. In this paper, we characterize the potentially K5-P4 and K5-Y4-graphic sequences where Y4 is a
On Potentially K5 - E3-graphic Sequences
TLDR
This paper characterize the potentially K5 − P3, K 5 − A3,K5 − K3 and K5- K1,3-graphic sequences where A3 is P2 ∪ K2 and pK2 is the matching consisted of p edges.
J an 2 00 8 On Potentially 3-regular graph graphic Sequences ∗
For given a graph H , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the
The Characterization for a Graphic Sequence to have a Realization Containing K1,1,s
TLDR
A simple characterization of potentially K1,1,s-graphic sequences for s ≥ 2 and n ≤ 3s + 1 is obtained and implies Lai’s conjecture on σ(K1, 1,s, n), which was confirmed by J.H. Yin, J.S. Li and W.Y. Li.
Potentially Km — G-graphical sequences: A survey
The set of all non-increasing nonnegative integer sequences π = (d(v1), d(v2), …, d(vn)) is denoted by NSn. A sequence π ∈ NSn is said to be graphic if it is the degree sequence of a simple graph G

References

SHOWING 1-10 OF 43 REFERENCES
On potentially (K4-e)-graphic sequences
TLDR
This characterization implies a theorem due to C. H. Lai and a characterization of potentially C4 Graphic sequences where K4 − e is the graph obtained from K4 by removing one edge.
The smallest degree sum that yields potentially fan graphical sequences
Let F_r be the fan with r vertices.For every n-term graphic sequence π=(d_1,d_2,…,d_n),it is proved that the smallest degree sum that yields potentially fan graphic sequences is σ(F_5,n)=4n-4,n≥5.
AN EXTREMAL PROBLEM ON POTENTIALLY $K_{r,r}$-ke-GRAPHIC SEQUENCES
TLDR
The identity for the graph obtained from the complete bipartite graph by deleting k edges which form a matching is determined.
A note on potentially K4-e graphical sequences
TLDR
This paper proves that $\sigma (K_4-e, n)=2[(3n-1)/2]$ for $n\geq 7$ and $n=4,5,$ and $\s Sigma(K-4- e, 6)= 20$.
Graphic Sequences with a Realization Containing a Friendship Graph
TLDR
For n sufficiently large, σ(Fk, n) is determine precisely, and it is shown that for any realizable degree sequence π, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph.
An extremal problem on the potentially Pk-graphic sequences
On the potentially Pk-graphic sequences
The Erds-Jacobson-Lehel conjecture on potentially P_k-graphic sequence is true
A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing
...
...