The linear complexity of a graph.
The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from {1, . . . , k}. A list assignment to G is an assignment L = {L(v)}v∈V (G) of lists of colors to the vertices of G. A distinguishing L-coloring of G is a distinguishing coloring of G where the color of each...
The list linear arboricity of planar graphs
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having Δ ≥ 13, or for any planar graph with Δ ≥ 7 and without i-cycles for some i ∈ {3,4,5}. We also prove that ⌈½Δ(G)⌉ ≤ lla(G) ≤ ⌈½(Δ(G)+1)⌉ for any planar graph having Δ ≥ 9.
The Littlewood-Richardson rule - the cornerstone for computing group properties
The local metric dimension of a graph
For an ordered set of distinct vertices in a nontrivial connected graph , the metric code of a vertex of with respect to is the -vector where is the distance between and for . The set is a local metric set of if for every pair of adjacent vertices of . The minimum positive integer for which has a local metric -set is the local metric dimension of . A local metric set of of cardinality is a local metric basis of . We characterize all nontrivial connected...
The Loebl-Komlós-Sós conjecture for trees of diameter 5 and for certain caterpillars.
The lollipop graph is determined by its spectrum.
The lonely runner with seven runners.
The Lotharingian impact on combinatorial mathematics: Myth or reality?
The lower tail of the random minimum spanning tree.
The MacNeille completion of the poset of partial injective functions.
The main part of the spectrum, divisors and switching of graphs.
The major counting of nonintersecting lattice paths and generating functions for tableaux. (Summary).
The many formulae for the number of Latin rectangles.
The map asymptotics constant .
The Markov chain asymptotics of random mapping graphs
The Markov-WZ method.
The matching polynomial of a distance-regular graph.
The Mathieu group and its pseudogroup extension .
The maximal spectral radius of a digraph with edges.