TY - JOUR
T1 - On Potentially Graphical Sequences of $G−E(H)$
AU - Bilal A. Chat & S. Pirzada
JO - Analysis in Theory and Applications
VL - 2
SP - 187
EP - 198
PY - 2018
DA - 2018/07
SN - 34
DO - http://doi.org/10.4208/ata.2018.v34.n2.8
UR - https://global-sci.org/intro/article_detail/ata/12586.html
KW - Graph, $(a,b,n)$-graph, potentially graphical sequences.
AB - <p style="text-align: justify;">A loopless graph on $n$ vertices in which vertices are connected at least by $a$ and at most by $b$ edges is called a $(a,b,n)$-graph. A $(b,b,n)$-graph is called $(b,n)$-graph
and is denoted by $K^b_n$ (it is a complete graph), its complement by $\overline{K}^b_n$. A non increasing
sequence $π = (d_1,···,d_n)$ of nonnegative integers is said to be $(a,b,n)$ graphic if it
is realizable by an $(a,b,n)$-graph. We say a simple graphic sequence $π = (d_1,···,d_n)$ is
potentially $K_4−K_2\cup K_2$-graphic if it has a a realization containing an $K_4−K_2\cup K_2$ as a
subgraph where $K_4$ is a complete graph on four vertices and $K_2\cup K_2$ is a set of independent
edges. In this paper, we find the smallest degree sum such that every $n$-term
graphical sequence contains $K_4−K_2\cup K_2$ as subgraph.</p>