Linear recognition of pseudo-split graphs

Two graphs G and H with the same vertex set V are P₄-isomorphic if every four vertices {a,b,c,d} \subseteq V$ induce a chordless path (denoted by P₄) in G if and only if they induce a P₄ in H. We call a graph split-perfect if it is P₄-isomorphic to a ...

Two graphs G and H with the same vertex set V are P₄- isomorphic if every four vertices {a, b, c, d} ⊆ V induce a chordless path (denoted by P₄) in G if and only if they induce a P₄ in H. We call a graph split-perfect if it is P₄-isomorphic to a split ...

A proper vertex coloring of a non-oriented graph G is linear if the graph induced by the vertices of any two color classes is a forest of paths. A graph G is linearly L-list colorable if for a given list assignment L={L(v):v@?V(G)}, there exists a ...