On Factors of a Graph
1977 ◽
Vol 29
(2)
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pp. 438-440
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Keyword(s):
F Factor
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Let G be a graph with multiple edges. Let f be a function from the vertex set V(G) of G to the non-negative integers. An f-factor of G is a spanning subgraph F of G such that the degree (valence) of each vertex x in F is f(x). A theorem of Fulkerson, Hoffman and McAndrew [1] gives necessary and sufficient conditions to have an f-factor for a graph G with the odd-cycle property; i.e., if G has the property that either any two of its odd (simple) cycles have a common vertex, or there exists a pair of vertices, one from each cycle, which is joined by an edge. They proved this theorem using integer programming techniques, with a rather long proof. We show that this is a corollary of Tutte's f-factor theorem.
2007 ◽
Vol 75
(3)
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pp. 447-452
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2014 ◽
Vol 13
(05)
◽
pp. 1350162
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Keyword(s):
2019 ◽
Vol 18
(08)
◽
pp. 1950160
Keyword(s):