Linear algorithm for optimal path cover problem on interval graphs
Information Processing Letters
Optimal covering of cacti by vertex-disjoint paths
Theoretical Computer Science
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Optimal path cover problem on block graphs and bipartite permutation graphs
Theoretical Computer Science
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
The path-partition problem in block graphs
Information Processing Letters
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Optimal path cover problem on block graphs
Theoretical Computer Science
Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization
Journal of the ACM (JACM)
Discrete Applied Mathematics
On the Structure of Graphs with Non-Surjective L(2,1)-Labelings
SIAM Journal on Discrete Mathematics
Labelling Cayley Graphs on Abelian Groups
SIAM Journal on Discrete Mathematics
Full Color Theorems for L(2,1)-Colorings
SIAM Journal on Discrete Mathematics
Construction of Large Graphs with No Optimal Surjective L(2,1)-Labelings
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Extremal problems on consecutive L(2,1)-labelling
Discrete Applied Mathematics
An extremal problem on non-full colorable graphs
Discrete Applied Mathematics
Finding a minimum path cover of a distance-hereditary graph in polynomial time
Discrete Applied Mathematics
Note: On the hole index of L(2,1)-labelings of r-regular graphs
Discrete Applied Mathematics
On Path Cover Problems in Digraphs and Applications to Program Testing
IEEE Transactions on Software Engineering
Graph labeling and radio channel assignment
Journal of Graph Theory
On island sequences of labelings with a condition at distance two
Discrete Applied Mathematics
Notes: A note on collections of graphs with non-surjective lambda labelings
Discrete Applied Mathematics
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
Hi-index | 0.04 |
A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G. The path covering number of G, denoted by P(G), is the minimum number of paths in a path covering of G. A k-L(2,1)-labeling of a graph G is a mapping f from V(G) to the set {0,1,...,k} such that |f(u)-f(v)|=2 if d"G(u,v)=1 and |f(u)-f(v)|=1 if d"G(u,v)=2. The L(2,1)-labeling number@l(G) of G is the smallest number k such that G has a k-L(2,1)-labeling. The purpose of this paper is to study path covering numbers and L(2,1)-labeling numbers of graphs. Our main work extends most of the results in [S.S. Adams, A. Trazkovich, D.S. Troxell, B. Westgate, On island sequences of labelings with a condition at distance two, Discrete Appl. Math. 158 (2010) 1-7] and can answer an open problem in [J. Georges, D.W. Mauro, On the structure of graphs with non-surjective L(2, 1)-labelings, SIAM J. Discrete Math. 19 (2005) 208-223].