Euler dynamic H-trails in edge-colored graphs

Figures & data

Fig. 1 The sequence $P=(v_1,e_1,v_2,e_6,e_5,v_4,e_4,v_3,e_3,e_2,v_1)$ is a closed Euler dynamic H-trail in G but there is no closed Euler H-trail in G.

Fig. 2 The graph $L_2^H(G)$ is hamiltonian but there is no closed Euler dynamic H-trail in G.

Fig. 3 In b, the continued edges are in M and the dashed edges are in M_J .

Fig. 4 G_u is a complete k_u -partite graph, for $u\in V(G)\setminus \left\{x_4\right\}$, and $G_{x_4}$ has a bipartite spanning subgraph but there is no closed Euler dynamic H-trail in G.