科研之友
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摘要
Let B be a bipartite graph. We obtain two new results as follows. (1) Suppose that u is an element of V(B) is a vertex such that N(B)(u) contains at least vertical bar N(B)(u)vertical bar - 1 odd vertices. Let f : V(B) -> N be the function such that f(u) = 1 and f(v) = inverted right perpendiculard(B)(v)/2inverted left perpendicular + 1 for v is an element of V(B)\u. Then B is f-choosable. (2) Suppose that u is an element of V(B) is a vertex such that every vertex in N(B)(u) is odd, and v is an element of V(B) is an odd vertex that is not adjacent to u. Let f : V(B) -> N be the function such that f (u) = 1 and f (v) = inverted right perpendiculard(B)(v)/2inverted left perpendicular and f (w) = inverted right perpendiculard(B) (w)/2inverted left perpendicular + 1 for w is an element of V(B)\{u, v}. Then B is f -choosable.
