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1 de nov. de 2012 · A graph is a quasi-line graph if for every vertex v, the set of neighbours of v is expressible as the union of two cliques. Such graphs are more general than line graphs, but less general than claw-free graphs. Here we give a construction for all quasi-line graphs; it turns out that there are basically two kinds of connected quasi-line graphs ...
1 de ene. de 1999 · We show here that every elementary graph is made up in a well-defined way of a line-graph of bipartite graph and some local augments consisting of complements of bipartite graphs. This yields a complete description of the structure of claw-free Berge graphs and a new proof of their perfectness.
1 de ene. de 1998 · 70. Lemma 2.3.LetD be a minimal connected dominating set of a claw-free graph. G, and let X be the vertices of D in two or more cliques of the subgraph induced. by D. Then, for any x e X, D- {x ...
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 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 ...
11 de may. de 2023 · Notice that the 3-prism is a claw-free cubic graph with its strong chromatic index being equal to 9. In the same paper, the authors left the problem whether this bound can be improved to 7. This paper solves this problem and the main result is the following theorem. Theorem 1.3. Let G be a claw-free subcubic graph.
1 de abr. de 2019 · For a claw-free graph H with c l ( H) = L ( G), we call G the preimage of H. A connected graph Φ is a closed trail if the degree of each vertex in Φ is even. A closed trail Φ in a graph G is called a spanning closed trail (SCT) if V ( G) = V ( Φ), and is called a dominating closed trail (DCT) if E ( G − V ( Φ)) = 0̸.
