A degree condition for graphs to be fractional ID-[a, b]-factor-critical

A neighborhood condition for fractional ID-[a, b]-factor-critical graphs

A graph G is fractional ID-[a, b]-factor-critical if G − I has a fractional [a, b]-factor for every independent set I of G. We extend a result of Zhou and Sun concerning fractional ID-k-factor-critical graphs.

Degree Conditions of Fractional ID-k-Factor-Critical Graphs

We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if G− I has a fractional k-factor for every independent set I of G. Some sufficient conditions for a graph to be fractional ID-k-factor-critical are studied in this paper. Furthermore, we show that the result is best possible in some sense. 2010 Mathematics Subject C...

A result on fractional ID-[a, b]-factor-critical graphs

A graphG is fractional ID-[a, b]-factor-critical ifG−I includes a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if α(G) ≤ 4b(δ(G)−a+1) (a+1)2+4b , then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that the result is best possible in some sense.

A Degree Condition For Graphs to Have Connected (g, f)-Factors

On the edge-connectivity of C_4-free graphs

Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...