On the structure of (P5 P 5 ,gem)-free graphs
We give a complete structure description of (P5 P 5 ,gem)-free graphs. By the results of a related paper, this implies bounded clique width for this graph class. Hereby, as usual, the P5 P 5 is the induced path with five vertices a,b,c,d,e a , b , c , d , e and four edges ab,bc,cd,de ab , bc , cd , de , and the gem  consists of a P4 P 4 a,b,c,d a , b , c , d with edges ab,bc,cd ab , bc , cd plus a universal vertex e  adjacent to a,b,c,d a , b , c , d .
clique width (p5 p 5 p5 p 5 p5 p 5 p 5 gem)-free graphs modules and homogeneous sets in graphs prime graphs modular decomposition