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» (k, )-Distance-Hereditary Graphs
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STACS
2010
Springer
14 years 3 months ago
The k-in-a-path Problem for Claw-free Graphs
Testing whether there is an induced path in a graph spanning k given vertices is already NP-complete in general graphs when k = 3. We show how to solve this problem in polynomial t...
Jirí Fiala, Marcin Kaminski, Bernard Lidick...
DM
2008
103views more  DM 2008»
13 years 8 months ago
Improper colouring of (random) unit disk graphs
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
Ross J. Kang, Tobias Müller, Jean-Séba...
COMBINATORICS
1999
95views more  COMBINATORICS 1999»
13 years 8 months ago
Maximum Degree Growth of the Iterated Line Graph
Let k denote the maximum degree of the kth iterated line graph Lk(G). For any connected graph G that is not a path, the inequality k+1 2k - 2 holds. Niepel, Knor, and Solt
Stephen G. Hartke, Aparna W. Higgins
DAM
2010
86views more  DAM 2010»
13 years 8 months ago
Minimum fill-in and treewidth of split+ke and split+kv graphs
In this paper we investigate how graph problems that are NP-hard in general, but polynomially solvable on split graphs, behave on input graphs that are close to being split. For t...
Federico Mancini
EJC
2010
13 years 8 months ago
Shilla distance-regular graphs
A Shilla distance-regular graph (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divide...
Jack H. Koolen, Jongyook Park