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Planar and Nonplanar Graphs
Eulerian and Hamiltonian Digraphs
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1-factor 2-cell embedding 4-coloring adjacency matrix arcs Assume bipartite graph block chromatic number coloring of G complete graph component of G configurations connected graph contradiction Corollary cubic graph cut-vertex cycle of G define denote Determine diam G digraph disconnected distinct vertices edge of G edge-reconstructible eigenvalues embedding of G equivalence classes eulerian circuit follows Four Color G contains G is connected G of order genus graph G graph of order hamiltonian cycle hamiltonian graphs hamiltonian path Hence homeomorphic implies incident induced subgraph internally disjoint isolated vertices isomorphic Kempe chain Let G line graph maximum minimum number nonadjacent vertices nonempty graph nonisomorphic obtained orbits partition permutation Petersen graph planar graph plane positive integer Proof Let Prove rad G result self-complementary subgraph of G subgraphs G subset Suppose tournament trail triangulation u-v path upper embeddable vertex set vertices of degree vertices of G