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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Jauhari, Mohammad Imam
Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang
Mathematics

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Problem of Maximum Matching in Non-Bipartite Graph Using Edmonds’ Cardinality Matching Algorithm and Its Applicationin the Battle of Britain Case Abrori, Muchammad; Jauhari, Mohammad Imam
CAUCHY Vol 5, No 4 (2019): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (983.546 KB) | DOI: 10.18860/ca.v5i4.4294

Abstract

Matching is a part of graph theory that discusses pair. A matching M is called to be maximum if M has the highest number of  elements. A blossom which is encountered in non-bipartite graph can cause failure in process of finding the maximum matching in non-bipartite graph. One of the algorithms that can be used to find a maximum matching in non-bipartite graph is Edmonds’ Cardinality Matching Algorithm. Shrinking process is done in each blossom Bi that is encountered to become pseudovertex bi, in a way that each blossom does not interfere the process of finding a maximum matching in non-bipartite graph. In order to accelerate the finding, simple greedy method is used to perform initialization of matching and BFS algorithm is also used in constructing an alternating tree in a non-bipartite graph.The research discussed the finding of maximum  matching in non-bipartite graph using Edmonds’ cardinality matching algorithm. In addition, this research gave a sample of its application in the resolution of The Battle of Britain case. The result obtained is a maximum matching in non-bipartite graph. The maximum matching obtained is a solution to the case of The Battle of Britain.
Co-Authors Muchammad Abrori