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INDEPENDENCE AND COVERINGS
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1-factor adjacency matrix ao-minimal ao(G Behzad and Chartrand bipartite Bondy cartesian product Chartrand 1971 chromatic number clique graph color connected graph contains converse is false cubic graph degree sequence denoted embedding example shows Figure following graph G and H G is connected G is hamiltonian genus graph G graph of G graph of order graph theory Greenwell and Hemminger hamiltonian graphs hamiltonian path hamiltonian-connected Harary Hemminger 1969 homomorphism independent set integer intersection graph Let G line cover line graph line isomorphism lines of G Manvel maximum minimum number n-connected non-adjacent points non-hamiltonian non-isomorphic number of G number of lines number of points oooo permutation groups Petersen graph planar graph point cover point line point-deleted subgraphs points of degree points of G Ramsey number reconstruction regular of degree set of points shown subgraph of G Take G THEOREM total chromatic total graph Tutte unique isometric tree vertex vertices