Geodesic
Decompositions of multigraphs into parts with the same size
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 335-347 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

Given a family ℱ of multigraphs without isolated vertices, a multigraph M is called ℱ-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of ℱ. We present necessary and sufficient conditions for existence of such decompositions if ℱ consists of all multigraphs of size q except for one. Namely, for a multigraph H of size q we find each multigraph M of size kq, such that every partition of the edge set of M into parts of cardinality q contains a part which induces a submultigraph of M isomorphic to H.
Keywords: edge decompositions, multigraphs 
@article{DMGT_2010_30_2_a12,
     author = {Ivanco, Jaroslav},
     title = {Decompositions of multigraphs into parts with the same size},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {335--347},
     year = {2010},
     volume = {30},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a12/}
}
TY  - JOUR
AU  - Ivanco, Jaroslav
TI  - Decompositions of multigraphs into parts with the same size
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2010
SP  - 335
EP  - 347
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a12/
LA  - en
ID  - DMGT_2010_30_2_a12
ER  - 
%0 Journal Article
%A Ivanco, Jaroslav
%T Decompositions of multigraphs into parts with the same size
%J Discussiones Mathematicae. Graph Theory
%D 2010
%P 335-347
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a12/
%G en
%F DMGT_2010_30_2_a12
Ivanco, Jaroslav. Decompositions of multigraphs into parts with the same size. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 335-347. http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a12/

[1] J. Ivanco, M. Meszka and Z. Skupień, Decompositions of multigraphs into parts with two edges, Discuss. Math. Graph Theory 22 (2002) 113-121, doi: 10.7151/dmgt.1162.

[2] W. Wang and K. Zhang, Equitable colorings of line graphs and complete r-partite graphs, Systems Science and Math. Sciences 13 (2000) 190-194.