Decomposition of bipartite graphs into closed trails

Cichacz, Sylwia, and Horňák, Mirko. "Decomposition of bipartite graphs into closed trails." Czechoslovak Mathematical Journal 59.1 (2009): 129-144. <http://eudml.org/doc/37912>.

@article{Cichacz2009,
abstract = {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.},
author = {Cichacz, Sylwia, Horňák, Mirko},
journal = {Czechoslovak Mathematical Journal},
keywords = {even graph; closed trail; graph arbitrarily decomposable into closed trails; bipartite graph; even graph; closed trail; graph arbitrarily decomposable into closed trails; bipartite graph},
language = {eng},
number = {1},
pages = {129-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Decomposition of bipartite graphs into closed trails},
url = {http://eudml.org/doc/37912},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Cichacz, Sylwia
AU - Horňák, Mirko
TI - Decomposition of bipartite graphs into closed trails
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 129
EP - 144
AB - 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.
LA - eng
KW - even graph; closed trail; graph arbitrarily decomposable into closed trails; bipartite graph; even graph; closed trail; graph arbitrarily decomposable into closed trails; bipartite graph
UR - http://eudml.org/doc/37912
ER -