
(Theta, triangle)free and (even hole, K_4)free graphs. Part 2 : bounds on treewidth
A theta is a graph made of three internally vertexdisjoint chordless p...
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Independent sets in (P_4+P_4,Triangle)free graphs
The Maximum Weight Independent Set Problem (WIS) is a wellknown NPhard...
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Structure and colour in trianglefree graphs
Motivated by a recent conjecture of the first author, we prove that ever...
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(Theta, triangle)free and (even hole, K_4)free graphs. Part 1 : Layered wheels
We present a construction called layered wheel. Layered wheels are graph...
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A simple combinatorial algorithm for restricted 2matchings in subcubic graphs – via halfedges
We consider three variants of the problem of finding a maximum weight re...
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Contains and Inside relationships within combinatorial Pyramids
Irregular pyramids are made of a stack of successively reduced graphs em...
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The complete set of minimal simple graphs that support unsatisfiable 2CNFs
A propositional logic sentence in conjunctive normal form that has claus...
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Maximum independent sets in (pyramid, even hole)free graphs
A hole in a graph is an induced cycle with at least 4 vertices. A graph is evenholefree if it does not contain a hole on an even number of vertices. A pyramid is a graph made of three chordless paths P_1 = a ... b_1, P_2 = a ... b_2, P_3 = a ... b_3 of length at least 1, two of which have length at least 2, vertexdisjoint except at a, and such that b_1b_2b_3 is a triangle and no edges exist between the paths except those of the triangle and the three edges incident with a. We give a polynomial time algorithm to compute a maximum weighted independent set in a evenholefree graph that contains no pyramid as an induced subgraph. Our result is based on a decomposition theorem and on bounding the number of minimal separators. All our results hold for a slightly larger class of graphs, the class of (square, prism, pyramid, theta, even wheel)free graphs.
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