DM
2007
13 years 4 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 4 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 4 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 4 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 4 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 4 months ago
2007
DM
2007
13 years 4 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 4 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 4 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 4 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...