Decompositions of multigraphs into parts with two edges

Jaroslav Ivančo; Mariusz Meszka; Zdzisław Skupień

Discussiones Mathematicae Graph Theory (2002)

  • Volume: 22, Issue: 1, page 113-121
  • ISSN: 2083-5892

Abstract

top
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 the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.

How to cite

top

Jaroslav Ivančo, Mariusz Meszka, and Zdzisław Skupień. "Decompositions of multigraphs into parts with two edges." Discussiones Mathematicae Graph Theory 22.1 (2002): 113-121. <http://eudml.org/doc/270217>.

@article{JaroslavIvančo2002,
abstract = {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 the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.},
author = {Jaroslav Ivančo, Mariusz Meszka, Zdzisław Skupień},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge decomposition; multigraph; line graph; 1-factor},
language = {eng},
number = {1},
pages = {113-121},
title = {Decompositions of multigraphs into parts with two edges},
url = {http://eudml.org/doc/270217},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Jaroslav Ivančo
AU - Mariusz Meszka
AU - Zdzisław Skupień
TI - Decompositions of multigraphs into parts with two edges
JO - Discussiones Mathematicae Graph Theory
PY - 2002
VL - 22
IS - 1
SP - 113
EP - 121
AB - 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 the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.
LA - eng
KW - edge decomposition; multigraph; line graph; 1-factor
UR - http://eudml.org/doc/270217
ER -

References

top
  1. [1] K. Bryś, M. Kouider, Z. Lonc and M. Mahéo, Decomposition of multigraphs, Discuss. Math. Graph Theory 18 (1998) 225-232, doi: 10.7151/dmgt.1078. Zbl0926.05028
  2. [2] Y. Caro, The decomposition of graphs into graphs having two edges, a manuscript. 
  3. [3] Y. Caro and J. Schönheim, Decompositions of trees into isomorphic subtrees, Ars Comb. 9 (1980) 119-130. Zbl0454.05022
  4. [4] J. Ivančo, M. Meszka and Z. Skupień; Decomposition of multigraphs into isomorphic graphs with two edges, Ars Comb. 51 (1999) 105-112. 
  5. [5] E.B. Yavorski, Representations of oriented graphs and φ-transformations [Russian], in: A. N. Sarkovski, ed., Theoretical and Applied Problems of Differential Equations and Algebra [Russian] (Nauk. Dumka, Kiev, 1978) 247-250. 
  6. [6] M. Las Vergnas, A note on matchings in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260. 
  7. [7] Z. Skupień; Problem 270 [on 2-edge-decomposable multigraphs], Discrete Math. 164 (1997) 320-321. 
  8. [8] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12. Zbl0293.05157

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.