Journal of Graph Theory
On a closure concept in claw-free graphs
Journal of Combinatorial Theory Series B
Closure and Hamiltonian-connectivity of claw-free graphs
Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
Searching minimal fractional graph factors by lattice based evolution
WSEAS Transactions on Information Science and Applications
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A graph G is said to be n-factor-critical if G - T has a perfect matching for every T ⊂ V(G) with |T| = n. For a vertex x of a graph G, local completion of G at x is the operation of joining every pair of nonadjacent vertices in NG(x). For a property P of graphs, a vertex x in a graph G is said to be P-eligible if the subgraph of G induced by NG(x) satisfies P but it is not complete. For a graph G, a graph H is said to be a P-closure of G if there exists a series of graphs G = G0, G1,..., Gr = H such that Gi is obtained from Gi-1 by local completion at some P-eligible vertex in Gi-1 and H = Gr has no P-eligible vertex. In this paper, we investigate the relation between factor-criticality and a P-closure, where P is a bounded independence number or a bounded domination number.