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GRAPHS AND SUBGRAPHS
CONNECTED AND DISCONNECTED GRAPHS
8 other sections not shown
1-factor 4-coloring acyclic adjacency matrix belongs bipartite graph chromatic number complete graph component of G connected graph consider contradiction Corollary cubic graph cut-vertex of G cut-vertices cycle of G define deleting denote determine disconnected edge-disjoint edges of G eigenvalues elements embedded eulerian circuit eulerian graph follows Four Color Problem G contains G E(H G is connected G of order G V(G G1 and G2 genus graph G graph of order graph theory hamiltonian cycle hamiltonian graphs homeomorphic implies induced subgraph isomorphic least Math minimum number multigraph n-connected nonempty graph nontrivial connected graph number of edges number of vertices obtained outerplanar paths in G planar graph plane positive integer PROBLEM SET Prove randomly eulerian region of G regular graph result subgraph of G subgraphs G subset Suppose Theorem triangle vertex of degree vertex set vertices of G