Abstract
A chain in a graph is essentially a continuous route in the graph, which does not repeat any edge. A finite chain is a circuit if its end vertices coincide; otherwise it is a trail. An infinite chain is a one-way chain if it has an end vertex; otherwise it is a two-way chain. A chain decomposition of a graph is a set of edge disjoint chains which together contain all edges of the graph. We develop a systematic foundation for studying chain decompositions, with particular attention to decomposition of an infinite graph into a minimal set of chains. We then survey the relevant known results.
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© 1984 Springer-Verlag
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Eggleton, R.B., Skilton, D.K. (1984). Chain decompositions of graphs, 1: Abstract graphs. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073128
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DOI: https://doi.org/10.1007/BFb0073128
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