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D. Hartvigsen recently gave an algorithm to find a C4-free 2-factor in a bipartite graph and using this algorithm he proved several nice theorems. Now we give a simple inductive proof for a generalization of his Tutte-type theorem, and prove the corresponding Ore-type theorem as well. The proof follows the idea of the inductive proof for the Hall's theorem given by Halmos and Vaughn.
Bibtex entry:
| AUTHOR | = | {Kir{\'a}ly, Zolt{\'a}n}, |
| TITLE | = | {$C_4$-free 2-factors in bipartite graphs}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2001}, |
| NUMBER | = | {TR-2001-13} |