a neighborhood :union: condition for fractional $(k,n',m)$-critical deleted graphs
نویسندگان
چکیده
a graph $g$ is called a fractional $(k,n',m)$-critical deleted graph if any $n'$ vertices are removed from $g$ the resulting graph is a fractional $(k,m)$-deleted graph. in this paper, we prove that for integers $kge 2$, $n',mge0$, $nge8k+n'+4m-7$, and $delta(g)ge k+n'+m$, if $$|n_{g}(x)cup n_{g}(y)|gefrac{n+n'}{2}$$ for each pair of non-adjacent vertices $x$, $y$ of $g$, then $g$ is a fractional $(k,n',m)$-critical deleted graph. the bounds for neighborhood :union: condition, the order $n$ and the minimum degree $delta(g)$ of $g$ are all sharp.
منابع مشابه
A NEIGHBORHOOD UNION CONDITION FOR FRACTIONAL (k, n′,m)-CRITICAL DELETED GRAPHS
A graph G is called a fractional (k, n′,m)-critical deleted graph if any n′ vertices are removed from G the resulting graph is a fractional (k,m)-deleted graph. In this paper, we prove that for integers k ≥ 2, n′,m ≥ 0, n ≥ 8k + n′ + 4m− 7, and δ(G) ≥ k + n′ +m, if |NG(x) ∪NG(y)| ≥ n+ n′ 2 for each pair of non-adjacent vertices x, y of G, then G is a fractional (k, n′,m)-critical deleted graph....
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عنوان ژورنال:
transactions on combinatoricsجلد ۶، شماره ۱، صفحات ۱۳-۱۹
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