TY  - JOUR
AU  - Lattanzio, John J. 
PY  - 2010
TI  - Edge Double-Critical Graphs
JF  - Journal of Mathematics and Statistics
VL  - 6
IS  - 3
DO  - 10.3844/jmssp.2010.357.358
UR  - https://thescipub.com/abstract/jmssp.2010.357.358
AB  - 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.