Decompositions of multigraphs into parts with two edges

• Autorzy: Jaroslav Ivančo , Mariusz Meszka , Zdzisław Skupień
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

edge decomposition; multigraph; line graph; 1-factor

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 113-121

Daty

wydano

2002

otrzymano

2000-10-04

poprawiono

2001-05-28

Twórcy

autor

Jaroslav Ivančo

• Department of Geometry and Algebra, Šafárik University, Jesenná 5, 041 54 Košice, Slovakia

autor

Mariusz Meszka

• Faculty of Applied Mathematics AGH, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krakó, Poland

autor

Zdzisław Skupień

• Faculty of Applied Mathematics AGH, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krakó, Poland

Bibliografia

• [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.
• [2] Y. Caro, The decomposition of graphs into graphs having two edges, a manuscript.
• [3] Y. Caro and J. Schönheim, Decompositions of trees into isomorphic subtrees, Ars Comb. 9 (1980) 119-130.
• [4] J. Ivančo, M. Meszka and Z. Skupień; Decomposition of multigraphs into isomorphic graphs with two edges, Ars Comb. 51 (1999) 105-112.
• [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] M. Las Vergnas, A note on matchings in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260.
• [7] Z. Skupień; Problem 270 [on 2-edge-decomposable multigraphs], Discrete Math. 164 (1997) 320-321.
• [8] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12.

Identyfikatory

DOI

10.7151/dmgt.1162