GERM
发表于 2025-3-21 19:34:31
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陈旧
发表于 2025-3-21 20:28:03
Basic Graph Theory,n of Königsberg (now Kaliningrad) in such a way as to cross over each of the seven bridges spanning the river Pregel once, and only once. Euler realized that the precise shapes of the island and the other three territories involved are not important; the solvability depends only on their connection
Macronutrients
发表于 2025-3-22 01:08:17
Algorithms and Complexity,r some basic aspects of graph theoretic algorithms such as, for example, the problem of how to represent a graph. Moreover, we need a way to formulate the algorithms we deal with. We shall illustrate and study these concepts quite thoroughly using two specific examples, namely Euler tours and acycli
使隔离
发表于 2025-3-22 04:41:21
Shortest Paths,e German motorway system in the official guide, the railroad or bus lines in a public transportation system, and the network of routes an airline offers are routinely represented by graphs. Therefore, it is obviously of great practical interest to study paths in such graphs. In particular, we often
四指套
发表于 2025-3-22 10:13:34
Spanning Trees,nt chapter, we will study this important class of graphs in considerably more detail. After some further characterizations of trees, we shall study another way of determining the number of trees on . vertices which actually applies more generally: it allows one to compute the number of spanning tree
谦虚的人
发表于 2025-3-22 16:18:55
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谦虚的人
发表于 2025-3-22 17:28:08
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追逐
发表于 2025-3-22 21:32:52
Combinatorial Applications,se ow theory to study disjoint paths in graphs, matchings in bipartite graphs, transversals of set families, the combinatorics of matrices, partitions of directed graphs, partially ordered sets, parallelisms of complete designs, and the supply and demand theorem. In particular, transversal theory ca
Wallow
发表于 2025-3-23 04:07:10
Connectivity and Depth First Search, method for determining the connected components of a graph: breadth first search (BFS). In the present chapter, we mainly treat algorithmic questions concerning .-connectivity and strong connectivity. To this end, we introduce a further important strategy for searching graphs and digraphs (besides
繁重
发表于 2025-3-23 09:32:33
Colorings,y the theorem of Brooks on vertex colorings and the theorem of Vizing on edge colorings. As an aside, we explain the relationship between colorings and partial orderings, and briefly discuss perfect graphs. Moreover, we consider edge colorings of Cayley graphs; these are graphs which are defined usi