Joko Prasetio, Arta Ekayanti
DOI: 10.24269/ed.v4i1.434 #### Abstract

This research aims to: (1) know the criteria of a graph that has a -factor, (2) know the conditions of a regular graph that has a 1-factorization , (3) know the conditions of a regular graph that has a 2-factorization.

This research is a qualitative descriptive study using the method of literature study or literature review where a study of books, scientific journals, and other literature languages is carried out relating to factorization on regular graphs. This research begins by discussing the definitions and examples of euler graphs and regular bipartite multigraphs. Next in reviewing the terms of a regular graph which has a 1-factorization and which has a 2-factorization, it starts by discussing the definition and theorem of matching on bipartite graphs, definitions and examples of factorization graphs, then discussing the proof of theorem of regular graphs that have a 1-factor and a regular graph which has a 2-factor.

The results of this study indicate that: (1) Graph  is said to be -factorable  or can be factored into -factor , if can be decomposed or be eksplained into spanning subgraphs , where each  has a -factor and is edge-disjoint from , that is 1)  2)  … n) = . (2) The condition for a graph that has a 1-factorization is, if the graph is a -regular bipartite multigraph, with . (3) The condition for a graph that has a 2-factorization is, if the graph is a -regular graph, with .

Key words: Bipartite graphs, Factorization, Decomposition, Regular graph.

#### References

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