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An odd graph is a finite graph all of whose vertices have odd degrees. A graph is decomposable into odd subgraphs if its edge set can be partitioned into subsets each of which induces an odd subgraph of . The minimum value of for which such a decomposition of exists is the odd chromatic index, ...
An odd graph is a graph whose vertex degrees are all odd. As introduced by Pyber in 1991, an odd edge‐covering of graph is a family of odd subgraphs that cover its edges. The minimum size of such family is denoted by . Answering a question raised by Pyber, Mátrai proved in 2006 that for every simple graph . In this study, we characterize the same inequality for the class of loopless...
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