Complex sentence: A "k"-critical graph is a critical graph with chromatic number "k"; a graph "G" with chromatic number "k" is "k"-vertex-critical if each of its vertices is a critical element.
Split into simpler sentences: A "k"-critical graph is a critical graph with chromatic number "k". A graph "G" with chromatic number "k" is "k"-vertex-critical if each of its vertices is a critical element.