Combinatorics and Graph TheorySpringer Science & Business Media, 3. 4. 2009 - 381 strán (strany) There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph. |
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Výsledky 1 - 5 z 82.
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... Examples of complete graphs. The empty graph on n vertices, denoted by En , is the graph of order n where E is the ... examples are shown in Figure 1.14. FIGURE 1.14 . Examples of regular graphs . 5. Cycles. 1.1 Introductory Concepts 11.
... Examples of complete graphs. The empty graph on n vertices, denoted by En , is the graph of order n where E is the ... examples are shown in Figure 1.14. FIGURE 1.14 . Examples of regular graphs . 5. Cycles. 1.1 Introductory Concepts 11.
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... example, such an isomorphism could be described as follows: {(a,1),(b,2),(c,8),(d,3),(e,7),(f,4),(g,6),(h,5)}. When two graphs G and H are isomorphic, it is not uncommon to simply say that G = H or that “G is H.” As you will see, we ...
... example, such an isomorphism could be described as follows: {(a,1),(b,2),(c,8),(d,3),(e,7),(f,4),(g,6),(h,5)}. When two graphs G and H are isomorphic, it is not uncommon to simply say that G = H or that “G is H.” As you will see, we ...
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... Examples Example, the surest method of instruction. ( b ) Your path from the previous question may not be your shortest such path . Prove that your actual distance from the President is at most one away from the shortest such distance ...
... Examples Example, the surest method of instruction. ( b ) Your path from the previous question may not be your shortest such path . Prove that your actual distance from the President is at most one away from the shortest such distance ...
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Strana 39
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Iné vydania - Zobraziť všetky
Combinatorics and Graph Theory John M. Harris,Jeffry L. Hirst,Michael J. Mossinghoff Obmedzený náhľad - 2000 |
Combinatorics and Graph Theory John Harris,Jeffry L. Hirst,Michael Mossinghoff Obmedzený náhľad - 2008 |
Combinatorics and Graph Theory John M. Harris,Jeffry L. Hirst,Michael J. Mossinghoff Obmedzený náhľad - 2013 |
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2-coloring adjacency matrix adjacent algorithm assignment axiom beads binomial coefficients bipartite graph blue color combinatorial complete graph compute contains contradiction convex countable cycle defined denote the number determine the number edges of G elements equivalent Erdős espousable Eulerian exactly example Exercise exists following theorem formula function graph G graph in Figure graph of order graph theory Hamiltonian identity implies inaccessible cardinal induction infinite sets integer König's Lemma labeled least Let G matrix nonempty nonnegative integer number of vertices objects obtain one-to-one ordinal pair partition path perfect matching permutation pigeonhole principle pigeons planar graph positive integer preference problem proof prove Ramsey numbers Ramsey's Theorem real number sequence Show spanning tree stable marriage problem stable matching subgraph subset Suppose uncountable vertex of G weakly compact cardinal well-ordered women