Toughness of -minor-free graphs.
Chen, Guantao; Egawa, Yoshimi; Kawarabayashi, Ken-ichi; Mohar, Bojan; Ota, Katsuhiro — 2011
The Electronic Journal of Combinatorics [electronic only]
Toughness of -minor-free graphs.
Star-Cycle Factors of Graphs
A spanning subgraph F of a graph G is called a star-cycle factor of G if each component of F is a star or cycle. Let G be a graph and f : V (G) → {1, 2, 3, . . .} be a function. Let W = {v ∈ V (G) : f(v) = 1}. Under this notation, it was proved by Berge and Las Vergnas that G has a star-cycle factor F with the property that (i) if a component D of F is a star with center v, then degF (v) ≤ f(v), and (ii) if a component D of F is a cycle, then V (D) ⊆ W if and only if iso(G − S) ≤ Σx∈S f(x) for all...
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