The following question is answered: given a crossing family F of odd subsets of an even-sized ground set V, what is the condition of the existence of a pairing M of the elements of V for which d_{M}(X)=1 for every X in F? We show that the pairing exists if and only if F does not have a specific configuration of 4 sets. We present a consequence related to the conjecture of Woodall on dijoins.
Bibtex entry:
@techreport{egres-07-10,
AUTHOR | = | {Kir{\'a}ly, Tam{\'a}s}, |
TITLE | = | {A result on crossing families of odd sets}, |
NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2007}, |
NUMBER | = | {TR-2007-10} |