## Congressus Numerantium, Volume 185 |

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adjacent apply assume auxiliaries bipartite graphs c(ei c(en c(vi c(vn c(vo chordal graphs chromatic number class of graphs closed neighborhood CM CM coloring Complete Bipartite Graphs complete graph Computer Congressus Numerantium conjectures connected cubic graph connected graph contradiction cut vertex cycle D-reduction delete denote detectable 3-tuple factorization detection number distance graph double split graphs ecc(C(S eigenvalues elements endpoints exist Figure Gargano genetic algorithm GI-complete Graffiti.pc graph classes graph isomorphism graph of order Graph Theory H H H Hence if-operation implies induced subgraph initial round integer labeled Lemma Let G lower bound Mathematics neighbors non-decreasing number of edges number of nodes obtain OTWh(p pair partition path perfect graphs permutation planar graphs primes problem Proof Proposition Ramanujan graphs Ramsey sets regular graphs resulting graph sequence solution split graph star graph t]-coloring Theorem 3.5 time-stamped graph total dominating set total domination number upper bound vertex set vertex transitive Z-cyclic DTWh(p