## Abstract We prove that a 2βconnected, outerplanar bipartite graph (respectively, outerplanar nearβtriangulation) with a list of colors __L__ (__v__ ) for each vertex __v__ such that $|L(v)|\geq\min\{{\deg}(v),4\}$ (resp., $|L(v)|\geq{\min}\{{\deg}(v),5\}$) can be __L__βlistβcolored (except when
On the colorings of outerplanar graphs
β Scribed by Weifan Wang
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 601 KB
- Volume
- 147
- Category
- Article
- ISSN
- 0012-365X
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Let C; be a graph, u a vertex of G, and G -{u) the subgraph of G obtained from G by removing the vertex u and all arcs incident with u. G-$1 is calted a point~e~eti~n of G. In f 51, Ulam conjectured that if G has at least three vertices, then G can be reconstructed (up to isomorphism) froin the coil
AND Bruce Reed Department of Combinatorics and Optimisation, University of Waterloo, Waterloo, Ontario, Canada
## Abstract We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geo