منابع مشابه
Line Graphs and Forbidden Induced Subgraphs
Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 olte s gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it consists of two complete graphs sharing exactly one common edge. In this paper, we show that a graph...
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Many graphs which are encountered in the study of graph theory are characterized by a type of configuration or subgraph they possess. However, there are occasions when such graphs are more easily defined or described by the kind of subgraphs they are not permitted to contain. For example, a tree can be defined as a connected graph which contains no cycles, and Kuratowski [22] characterized plan...
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The graph theoretic problem of identifying the finite sets C of constraint graphs for which there is a countable universal C-free graph is closely related to the problem of determining for which sets C the model companion T ∗ C of the theory of C-free graphs is א0-categorical, and this leads back to combinatorics. Little is known about these theories from any other perspective, such as stabilit...
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Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...
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Let H be a family of connected graphs. A graph G is said to be H-free if G is H-free for every graph H in H. In [1] it was pointed that there is a family of connected graphs H not containing any induced subgraph of the claw having the property that the set of H-free connected graphs containing a claw is finite, provided also that those graphs have minimum degree at least two and maximum degree ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00459-9