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On reconstructing maximal outerplanar graphs

✍ Scribed by William B. Giles

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
421 KB
Volume
8
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 coilectinn of ati subgraphs G -{u] for u a vertex of G. f 41 contains many references relating to work on this conjecture; in addition, it is proved for o~~te~~an~ maths in [ 1 f .

Harary [ 2f conjectured that if G has at least four vertices, then it can actually be rwonstructed from the isomorphism types of its pointdeletions, ~th~~~t kn~~w~edg~~ of their mu~tip~~citie~. In 4 , Manvel pmed the Harary conjecture for maximal outerplanar graphs. The rersult of the present paper is the following strengthening of the theorem of Manvel :

πŸ“œ SIMILAR VOLUMES

Centers of maximal outerplanar graphs
Centers of maximal outerplanar graphs
✍ Andrzej Proskurowski πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 178 KB

## Abstract The center of a graph is defined to be the subgraph induced by the set of vertices that have minimum eccentricities (i.e., minimum distance to the most distant vertices). It is shown that only seven graphs can be centers of maximal outerplanar graphs.

On list-coloring outerplanar graphs
On list-coloring outerplanar graphs
✍ Joan P. Hutchinson πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 162 KB

## Abstract We prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) 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__‐list‐colored (except when