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» (k, )-Distance-Hereditary Graphs
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STACS
2010
Springer
15 years 6 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»
14 years 12 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»
14 years 11 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»
14 years 12 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
14 years 12 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