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Elementary Graphs and Decomposition Theory,matching-extendable graphs. However, we concentrate on three families of such graphs, ., 1-. and ., where each family is a subset of later family. There are two reasons for investing time on these families: firstly, we want to have better understanding of their structures and properties, including m

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-Extendable Graphs and ,-Factor-Critical Graphs,t turns out that only two classes of graphs, i.e., the complete graphs . and the complete bipartite graphs ., satisfy this property. Clearly, the property is very strong since we asked that the matchings of . size have to extend to a 1-factor. If we relax the property a bit by requiring only the mat

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https://doi.org/10.1007/978-3-531-92220-1In this chapter, we study properties and structures of .-extendable graphs and .-factor-critical graphs. By studying extremal graphs, either maximal or minimal, we are able to obtain effectively more understanding of the graphs, just as applying the extremal technique to other graph theory problems.

Rankle

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Extremal ,-Extendable Graphs and Generalizations,In this chapter, we study properties and structures of .-extendable graphs and .-factor-critical graphs. By studying extremal graphs, either maximal or minimal, we are able to obtain effectively more understanding of the graphs, just as applying the extremal technique to other graph theory problems.

高谈阔论

Fractional Factors of Graphs,In this chapter, we discuss another generalization of factors, i.e., fractional factors, from the perspective of fractional edges instead of integer edges.

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https://doi.org/10.1007/978-3-663-10799-6ence and communication networking. In the mean time, there are many new terminologies and knowledge accumulated in the process. So there are often more than one names or notions defined for a same entity. We list the terms and notions frequently used in this book and hope to provide readers with a consistent reference.

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Choreography

Factors and Graphic Parameters,es and properties of graphs from different perspectives, it is quite common in graph theory to investigate the links among the parameters. In this chapter, we investigate the relationships between graph factors and some popular parameters, such as toughness, binding number, connectivity and minimum degree, etc.