Let ${\rm Lct}(G)$ denote the set of all lengths of closed trails that exist in an even graph $G$. A sequence $(t_1,\dots ,t_p)$ of elements of ${\rm Lct}(G)$ adding up to $|E(G)|$ is $G$-realisable provided there is a sequence $(T_1,\dots ,T_p)$ of pairwise edge-disjoint closed trails in $G$ such that $T_i$ is of length $t_i$ for $i=1,\dots ,p$. The graph $G$ is arbitrarily decomposable into closed trails if all possible sequences are $G$-realisable. In the paper it is proved that if $a\ge 1$ is an odd integer and $M_{a,a}$ is a perfect matching in $K_{a,a}$, then the graph $K_{a,a}-M_{a,a}$ is arbitrarily decomposable into closed trails.
This article examines whether there are any differences in the way in which married couples and unmarried cohabitating couples manage their incomes. Using data from the ISSP 1994 and the ISSP 2002 the author attempts to answer the question of whether over the course of the 1990s in the Czech Republic the character of unmarried cohabitation changed, and whether the economic arrangements of unmarried couples with children resemble those of married couples. Crosstabulation indicates that unmarried couples manage their respective incomes separately more often than married couples do. However, if we take into account the different socio-demographic and socio-economic structures of these couples, the differences in income management connected with marital status vanish. The results of a logistic regression show that separate financial management occurs more often among childless couples, people less satisfied with their family life, and those who have experienced the break-up of a partnership before. In the case where an unmarried couple is raising children, the household income arrangement of the partners is similar to that of married couples.