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DM
2007
106views more  DM 2007»
10 years 2 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»
10 years 2 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»
10 years 2 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»
10 years 2 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»
10 years 2 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»
10 years 2 months ago
Edge-dominating cycles in graphs
Shinya Fujita, Akira Saito, Tomoki Yamashita
DM
2007
119views more  DM 2007»
10 years 2 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»
10 years 2 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»
10 years 2 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»
10 years 2 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
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