Decomposition of odd-hole-free graphs by double star cutsets and 2-joins

Decomposition of odd-hole-free graphs by double star cutsets and 2-joins

Decomposition of even-hole-free graphs with star cutsets and 2-joins

In this paper we consider the class of simple graphs defined by excluding, as inducedsubgraphs, even holes (i.e. chordless cycles of even length). These graphs are known aseven-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, thatuses star cutsets and 2-joins. This is a significant strengthening of the only other pre-viously known decomposition of ev...

Even-hole-free graphs part I: Decomposition theorem

We prove a decomposition theorem for even-hole-free graphs. The decompositions used are 2-joins and star, double-star and triple-star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even-hole-free graphs.

On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges‎

‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

Decomposing and Clique-Coloring (Diamond, Odd-Hole)-Free Graphs

A diamond is a graph on 4 vertices with exactly one pair of non-adjacent vertices, and an odd hole is an induced cycle of odd length. If G,H are graphs, G is H-free if no induced subgraph of G is isomorphic to H. A clique-colouring of G is an assignment of colours to the vertices of G such that no inclusion-wise maximal clique of size at least 2 is monochromatic. We show that every (diamond, od...