By Reinhard Diestel

ISBN-10: 3540609180

ISBN-13: 9783540609186

Best graph theory books

New PDF release: Graphs and Networks: Transfinite and Nonstandard

This self-contained e-book examines effects on transfinite graphs and networks accomplished via a continual study attempt prior to now numerous years. those new effects, masking the mathematical conception of electric circuits, are assorted from these provided in formerly released books by way of the writer, Transfiniteness for Graphs, electric Networks, and Random Walks and Pristine Transfinite Graphs and Permissive electric Networks.

Get Algorithmic Graph Theory and Perfect Graphs PDF

Algorithmic Graph idea and ideal Graphs, first released in 1980, has develop into the vintage creation to the sphere. This new Annals version maintains to express the message that intersection graph versions are an important and critical software for fixing real-world difficulties. It continues to be a stepping stone from which the reader may possibly embark on one of the interesting examine trails.

Read e-book online An Introduction to Catalan Numbers PDF

This textbook offers an advent to the Catalan numbers and their impressive homes, in addition to their a number of purposes in combinatorics. Intended to be available to scholars new to the topic, the e-book starts with extra simple issues earlier than progressing to extra mathematically subtle themes.

Extra info for Graph Theory

Example text

Nr ; if n1 = . . = nr =: s, we abbreviate this to Ksr . ) Graphs of the form K1,n are called stars. ,nr Ksr star = Fig. 2. Three drawings of the bipartite graph K3,3 = K32 Clearly, a bipartite graph cannot contain an odd cycle, a cycle of odd length. 1. A graph is bipartite if and only if it contains no odd cycle. 2 ] Proof . Let G = (V, E) be a graph without odd cycles; we show that G is bipartite. Clearly a graph is bipartite if all its components are bipartite or trivial, so we may assume that G is connected.

3, T has n − 1 edges, so m − n + 1 edges of G lie outside T . For each of these m − n + 1 edges e ∈ E E(T ), the graph T + e contains a cycle Ce (see Fig. 1 (iv)). Since none of the edges e lies on Ce for e = e, these m − n + 1 cycles are linearly independent. 3). Since none of the edges e ∈ T lies in De for e = e, these n − 1 cuts are linearly independent. 3) 24 1. The Basics e Fig. 3. The cut De incidence matrix The incidence matrix B = (bij )n×m of a graph G = (V, E) with V = { v1 , . . , vn } and E = { e1 , .

Show that the elements of the cycle space of a graph G are precisely the unions of the edges sets of edge-disjoint cycles in G. 28 1. The Basics 25. Given a graph G, ﬁnd among all cuts of the form E(v) a basis for the cut space of G. 26. Prove that the cycles and the cuts in a graph together generate its entire edge space, or ﬁnd a counterexample. 27. 6 generate the cycle space. 28. 6 generate the cut space. 29. What are the dimensions of the cycle and the cut space of a graph with k components?