Further results on Erdős–Faber–Lovász conjecture

Figures & data

Fig. 1 All graphs satisfying the hypothesis of the conjecture for n $=$ 3.

Fig. 2 4 copies of $K_4$.

Fig. 3 Construction of $H^2$ from $H^1,B_2$.

Fig. 4 Construction of $H^3$ from $H^2,B_3$.

Fig. 5 Construction of $H^4$ from $H^3,B_4$.

Fig. 6 $H_6$.

Fig. 7 Graph $G$, before and after relabeling the vertices.

Fig. 8 Splitting the common vertices of $H_4$ which are not in $N_2$.

Fig. 9 Graph $G^{\prime }$.

Fig. 10 A coloring of $H_6$ with six colors . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 11 Graph $G$: before and after relabeling the vertices.

Fig. 12 Graph $\hat{H}$.

Fig. 13 The graphs $\hat{H}$ and $G$, after colors have been assigned to their vertices . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 14 Graph $G$: before and after relabeling the vertices.

Fig. 15 Graph $\hat{H}$.

Fig. 16 The graphs $\hat{H}$ and $G$, after colors have been assigned to their vertices . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)