Geodesic
Chromatically unique multibridge graphs
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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Let $\theta(a_1,a_2,\cdots,a_k)$ denote the graph obtained by connecting two distinct vertices with $k$ independent paths of lengths $a_1,a_2,$ $\cdots,a_k$ respectively. Assume that $2\le a_1\le a_2\le \cdots \le a_k$. We prove that the graph $\theta(a_1,a_2, \cdots,a_k)$ is chromatically unique if $a_k < a_1+a_2$, and find examples showing that $\theta(a_1,a_2, \cdots,a_k)$ may not be chromatically unique if $a_k=a_1+a_2$.
DOI : 10.37236/1765
Classification : 05C15
Mots-clés : chromatic polynomials, polygon-tree 
@article{10_37236_1765,
     author = {F. M. Dong and K. L. Teo and C. H. C. Little and M. Hendy and K. M. Koh},
     title = {Chromatically unique multibridge graphs},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1765},
     zbl = {1031.05047},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1765/}
}
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F. M. Dong; K. L. Teo; C. H. C. Little; M. Hendy; K. M. Koh. Chromatically unique multibridge graphs. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1765

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