A stochastic complex network model society.
A strengthening of Brooks' Theorem for line graphs.
A strongly non-Ramsey uncountable graph
It is consistent that there exists a graph X of cardinality such that every graph has an edge coloring with colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).
A structural property of planar graphs and the simultaneous colouring of their edges and faces
A study of Eulerian numbers for permutations in the alternating group.
A study on the relationship between connecting different types of nodes and disassortativity by degree.
A Sufficient Condition for a Graph to Be Hamiltonian.
A sufficient condition for graphs with 1-factors
A sufficient condition for Hamiltonian graphs
A sufficient condition for the existence of k-kernels in digraphs
In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with l(γ) ≢ 0 (mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has four short chords. Then D has a k-kernel. This result generalizes some previous results...
A survey of algebra of tournaments.
A survey of hereditary properties of graphs
In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.
A survey of minimum saturated graphs.
A survey of pseudo (v, k, ...)-designs.
A survey of stack-sorting disciplines.
A Survey of the Path Partition Conjecture
The Path Partition Conjecture (PPC) states that if G is any graph and (λ1, λ2) any pair of positive integers such that G has no path with more than λ1 + λ2 vertices, then there exists a partition (V1, V2) of the vertex set of G such that Vi has no path with more than λi vertices, i = 1, 2. We present a brief history of the PPC, discuss its relation to other conjectures and survey results on the PPC that have appeared in the literature since its first formulation in 1981.
A survey on combinatorial optimization in dynamic environments∗
This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...
A survey on combinatorial optimization in dynamic environments∗
This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...
A survey on packing and covering problems in the Hamming permutation space.
A symbolic operator approach to power series transformation-expansion formulas.