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1 de nov. de 2008 · Introduction The main goal of this series of papers is to prove a theorem describing how to build the “most general” claw-free graph. In earlier papers, particularly in [4], we proved that every claw-free graph either belongs to one of a few basic classes that were we able to describe explicitly, or it admits one of a few kinds of ...
Figure 1: Claw-free cubic graphs with only 9 perfect matchings. We prove that every claw-free cubic n-vertex graph with no cutedge has more than 2n/12 perfect matchings. The graph should not have any cutedge; in Figure 1, we provide an example of a claw-free cubic graph with only 9 perfect matchings. Our approach is to use the structure of 2 ...
1 de sept. de 2008 · A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful w
A graph Gis claw-free if no induced subgraph is the bipartite graph K 1,3. An independent set of a graph Gis a set of nonadjacent vertices. The independence sequence of a claw-free graph is log-concave: for all 1 ≤k≤ℓ, the numbers I j of independent sets of size jsatisfies that I k−1I ℓ+1 ≤I kI ℓ.
27 de nov. de 2023 · A graph $G$ of order $n$ is said to be $k$-factor-critical for integers $1\leq k< n$, if the removal of any $k$ vertices results in a graph with a perfect matching.
25 de dic. de 2023 · A. Brandstaedt, F. Dragan On linear and circular structure of (claw, net)-free graph To appear in Discrete Appl. Math. []
A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way.
