DM
2007
13 years 10 months ago
2007
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...
DM
2007
13 years 10 months ago
2007
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...
DM
2007
13 years 10 months ago
2007
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 ...
DM
2007
13 years 10 months ago
2007
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...
DM
2007
13 years 10 months ago
2007
—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...
DM
2007
13 years 10 months ago
2007
DM
2007
13 years 10 months ago
2007
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...
DM
2007
13 years 10 months ago
2007
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 ...
DM
2007
13 years 10 months ago
2007
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...
DM
2007
13 years 10 months ago
2007
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...