Graphs and Combinatorics

, Volume 30, Issue 4, pp 933–947 | Cite as

Vertex-Colored Encompassing Graphs

  • Michael Hoffmann
  • Csaba D. Tóth
Original Paper


It is shown that every disconnected vertex-colored plane straight line graph with no isolated vertices can be augmented (by adding edges) into a connected plane straight line graph such that the new edges respect the coloring and the degree of every vertex increases by at most two. The upper bound for the increase of vertex degrees is best possible: there are input graphs that require the addition of two new edges incident to a vertex. The exclusion of isolated vertices is necessary: there are input graphs with isolated vertices that cannot be augmented to a connected vertex-colored plane straight line graph.


Planar straight line graph Encompassing graph Graph augmentation 


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceETH ZürichZurichSwitzerland
  2. 2.Department of MathematicsCalifornia State UniversityNorthridgeUSA
  3. 3.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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