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DM
2007
106views more  DM 2007»
13 years 11 months ago
The Roberts characterization of proper and unit interval graphs
In this note, a constructive proof is given that the classes of proper interval graphs and unit interval graphs coincide, a result originally established by Fred S. Roberts. Addit...
Frédéric Gardi
DM
2007
100views more  DM 2007»
13 years 11 months ago
Improved bounds on acyclic edge colouring
We prove that the acyclic chromatic index a (G) 6 for all graphs with girth at least 9. We extend the same method to obtain a bound of 4.52 with the girth requirement g 220. We al...
Rahul Muthu, N. Narayanan, C. R. Subramanian
DM
2007
149views more  DM 2007»
13 years 11 months ago
Even subgraphs of bridgeless graphs and 2-factors of line graphs
By Petersen’s theorem, a bridgeless cubic multigraph has a 2-factor. H. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing ...
Bill Jackson, Kiyoshi Yoshimoto
DM
2007
74views more  DM 2007»
13 years 11 months ago
Parameters for which the Griesmer bound is not sharp
7 We prove for a large class of parameters t and r that a multiset of at most t d−k + r d−k−2 points in PG(d, q) that blocks every k-dimensional subspace at least t times mu...
Andreas Klein, Klaus Metsch
DM
2007
114views more  DM 2007»
13 years 11 months ago
An inequality for the group chromatic number of a graph
—We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality...
Hong-Jian Lai, Xiangwen Li, Gexin Yu
DM
2007
66views more  DM 2007»
13 years 11 months ago
Edge-dominating cycles in graphs
Shinya Fujita, Akira Saito, Tomoki Yamashita
DM
2007
119views more  DM 2007»
13 years 11 months ago
Short proofs for cut-and-paste sorting of permutations
We consider the problem of determining the maximum number of moves required to sort a permutation of [n] using cut-and-paste operations, in which a segment is cut out and then pas...
Daniel W. Cranston, Ivan Hal Sudborough, Douglas B...
DM
2007
98views more  DM 2007»
13 years 11 months ago
p-adic valuations and k-regular sequences
A sequence is said to be k-automatic if the nth term of this sequence is generated by a finite state machine with n in base k as input. Regular sequences were first defined by ...
Jason P. Bell
DM
2007
113views more  DM 2007»
13 years 11 months ago
Counting labeled general cubic graphs
Recurrence relations are derived for the numbers of labeled 3-regular graphs with given connectivity, order, number of double edges, and number of loops. This work builds on metho...
Gab-Byung Chae, Edgar M. Palmer, Robert W. Robinso...
DM
2007
125views more  DM 2007»
13 years 11 months ago
Generalized switch-setting problems
Switch-setting games like Lights Out are typically modelled as a graph, where the vertices represent switches and lamps, and the edges capture the switching rules. We generalize t...
Torsten Muetze