## A First Course in Graph TheoryThis comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications. Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols. |

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1-factor 3-regular graph assume bipartite graph blue chromatic number complete graph component of G connected graph Cube cut-vertex cut-vertices degree sequence degv diam(G digraph distinct vertices dominating set edges of G embedded Erd˝os Eulerian circuit Exercises for Section exists follows Four Color G and H G contains G is connected G of Figure G of order G1 and G2 Give an example graph contains graph G graph in Exercise graph of order graph theory Hamiltonian cycle Hamiltonian graph Hamiltonian path induced subgraph integer isomorphic labeled Let G mathematician mathematics minimum spanning tree nonadjacent vertices nonempty nonplanar nontrivial connected graph number of G pair partite sets Petersen graph planar graph positive integer problem Prove r-regular Ramsey number red-blue coloring regions shown in Figure Solution subgraph of G subset torus tournament tree of order vertex set vertices of degree vertices of G