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发表于 2025-3-21 19:34:31 | 显示全部楼层 |阅读模式
书目名称Graphs, Networks and Algorithms
编辑Dieter Jungnickel
视频videohttp://file.papertrans.cn/389/388179/388179.mp4
丛书名称Algorithms and Computation in Mathematics
图书封面Titlebook: ;
出版日期Textbook 2013Latest edition
版次4
doihttps://doi.org/10.1007/978-3-642-32278-5
isbn_softcover978-3-642-43664-2
isbn_ebook978-3-642-32278-5Series ISSN 1431-1550
issn_series 1431-1550
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发表于 2025-3-21 20:28:03 | 显示全部楼层
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
发表于 2025-3-22 01:08:17 | 显示全部楼层
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
发表于 2025-3-22 04:41:21 | 显示全部楼层
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
发表于 2025-3-22 10:13:34 | 显示全部楼层
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
发表于 2025-3-22 16:18:55 | 显示全部楼层
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发表于 2025-3-22 21:32:52 | 显示全部楼层
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
发表于 2025-3-23 04:07:10 | 显示全部楼层
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
发表于 2025-3-23 09:32:33 | 显示全部楼层
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
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