DM
2008
13 years 9 months ago
2008
Let G be the set that contains precisely the graphs on n vertices with maximum degree 3 for which there exists a 4-cycle system of their complement in Kn. In this paper G is compl...
DM
2008
13 years 9 months ago
2008
We prove that a K4-free graph G of order n, size m and maximum degree at most three has an independent set of cardinality at least 1 7 (4n - m - - tr) where counts the number of c...
DM
2010
13 years 9 months ago
2010
For a graph G, denote by fk(G) the smallest number of vertices that must be deleted from G so that the remaining induced subgraph has its maximum degree shared by at least k verti...
DM
2010
13 years 9 months ago
2010
We show that the firefighter problem is NP-complete for cubic graphs. We also show that given a rooted tree of maximum degree three in which every leaf is the same distance from t...
DM
2010
13 years 10 months ago
2010
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
ALGORITHMICA
2008
13 years 10 months ago
2008
We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree with max{, 9} colors. Thus...
ESA
2010
Springer
13 years 11 months ago
2010
Springer
Abstract. In a seminal STOC'95 paper, Arya et al. [4] devised a construction that for any set S of n points in Rd and any > 0, provides a (1 + )-spanner with diameter O(lo...
SIROCCO
2000
13 years 11 months ago
2000
A graph with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, but it has been conje...
CCCG
2006
13 years 11 months ago
2006
We show that any tree whose maximum degree is at most 10 can be drawn in 3-space such that it is the minimum spanning tree of its vertices.
SODA
2008
ACM
13 years 11 months ago
2008
ACM
Let H be a finite family of graphs. A graph G is H-universal if it contains a copy of each H H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum d...