@article {10.3844/jmssp.2010.357.358, article_type = {journal}, title = {Edge Double-Critical Graphs}, author = {Lattanzio, John J.}, volume = {6}, year = {2010}, month = {Sep}, pages = {357-358}, doi = {10.3844/jmssp.2010.357.358}, url = {https://thescipub.com/abstract/jmssp.2010.357.358}, abstract = {Problem statement: The vertex double-critical conjecture that the only vertex double-critical graph is the complete graph has remained unresolved for over forty years. The edge analogue of this conjecture has been proved. Approach: It was observed that if the chromatic number decreases by two upon the removal of a 2-matching, then the 2-matching comprises four vertices which determine an induced subgraph isomorphic to the complete graph on four vertices. This observation was generalized to t-matchings. Results: In this note, it has been shown that the only edge double-critical graph is the complete graph. Conclusion/Recommendations: An alternate proof that the only edge double-critical graph is the complete graph has been obtained. Moreover, the result has been obtained independently.}, journal = {Journal of Mathematics and Statistics}, publisher = {Science Publications} }