triangle-free graphs
The four-in-a-tree problem in triangle-free graphs
... 4-in-a-tree, triangle-free graphs 1 Introduction Many interesting classes of graphs are defined by forbidding induced subgraphs, see [2] for a ...
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Enumerating Minimal Dominating Sets in Triangle-Free Graphs
... in triangle-free graphs, the generation of all potential extensions of a partial minimal dominating set to a new neighborhood is closely related to the enumeration of minimal dominating sets in split ...
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Colouring vertices of triangle-free graphs without forests
... planar graphs [ 11 ], 4-colourability is NP-complete for graphs containing no induced path on 8 vertices [ 7 ], vertex colouring is NP-complete for line graphs [ 16 ...for graphs in some ...
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On the size of identifying codes in triangle-free graphs
... In order to prove our main result, we show how to build (large enough) independent sets in triangle-free graphs such that the three first conditions of Proposition 2 hold (see Lemma 10). However, it ...
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Triangle‐free graphs that do not contain an induced subdivision of K 4 are 3‐colorable
... {x, y} ∩ V (C k ) 6= ∅. Now consider the bipartite graph G ′ , which (roughly speaking) is the graph obtained from G \ {s} by contracting V (C k ) ∪ N k to a single vertex z if |V (C k )| > 1. It turns out that G ′ is ...
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On wheel-free graphs
... of triangle- free graphs with arbitrarily large chromatic number, due to Zykov [18], shows that the constant c in the first question must be at least ...of graphs with no wheels as induced ...
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Claw-Free Graphs With Strongly Perfect Complements. Fractional and Integral Version. Part I. Basic graphs
... Resolved graphs and trigraphs; finding dominant cliques We say that a claw-free trigraph T is resolved if every F -free graphic thickening of T is ...
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Decomposition, approximation, and coloring of odd-minor-free graphs
... odd-minor-free graphs. Specifically, we prove that every odd-minor-free graph can be decom- posed into a clique-sum of “almost-bipartite” graphs and graphs that are “almost-embeddable” ...
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triangle rectangle
... Le triangle rectangle HSA 2 ayant des petits côtés de longueurs r 1 et r 2 est semblable à ...Le triangle rectangle UAT est semblable à ABC (mêmes angles, car un côté commun et les deux autres côtés sont ...
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triangle équilatéral
... Le triangle CIJ peut-il être équilatéral ? La construction n'est pas unique, il s'agit d'en réaliser au moins une aboutissant à un triangle équilatéral inscrit dans le ...
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Recognition of C4-free and 1/2-hyperbolic graphs
... 40]. We inform the reader that Definition 1 is not a universal definition for the hyperbolicity of a graph. Some authors actually proposed and studied other definitions (see, for instance [13, 23]). Though the value of ...
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triangle
... La démonstration se fait facilement en montrant que les aires des triangles ABP et ABC sont égales (bases de même longueur et hauteur commune), ainsi que AQP et ABP. Si I, J et K sont les points d'intersection des ...
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Vertex partitions of ($C 3 , C 4 , C 6$) -free planar graphs
... most k 2 . Choi, Liu, and Oum [ 1 ] have established that there exists exactly two minimal sets of forbidden cycle length such that every planar graph is (0, k)- colorable for some absolute constant k. • planar ...
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Parameterized Complexity of Independent Set in H-free graphs
... The cycle cliques adjacent to one path clique are called branching cliques. Finally, 157[r] ...
Maximum independent sets in (pyramid, even hole)-free graphs
... the triangle and the three edges incident with ...even-hole-free graphs places significant restrictions on its structure. The graphs seems to ”organize itself” around the pyramid, in a way ...
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Distance and routing labeling schemes for cube-free median graphs
... vertices. First, the algorithm computes a centroid (median) vertex c of G and the star St(c) of c (the union of all edges and squares of G incident to c). The star St(c) is gated, i.e., each vertex of G has a unique ...
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On the recognition of $C_4$-free and $1/2$-hyperbolic graphs
... -hyperbolic graphs can be recognized in linear-time, for some classes of graphs for which detecting an induced quadrangle is easy, like for instance planar graphs ...-hyperbolic graphs, as the ...
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Triangle inscrit dans un carré
... Le triangle AB’C’ formé de deux côtés et d'une diagonale est minimal. En appelant B 1 le deuxième point d'intersection d'une autre sécante (BC) avec le parallélogramme, on compare, dans la configuration de la ...
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Contraction decomposition in h-minor-free graphs and algorithmic applications
... on graphs of bounded ...low-treewidth graphs—see, ...bounded-treewidth graphs may also be ...H-minor-free graphs), whereas on general graphs the problem is inapproximable within ...
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Retraites: un triangle d’incompatibilité
... Mais telle qu’annoncée, avec ses promesses contradictoires aggravées depuis par les concessions faites aux uns et aux autres, cette réforme n’était pas soutenable, on peut même parler d’un triangle ...
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