In a recent article Agrawal et al. (STACS 2016) studied a simultaneous variant of the classic Feedback Vertex Set problem, called Simultaneous Feedback Vertex Set (Sim-FVS). In this problem the input is an n-vertex graph G, an integer k and a coloring function col : E(G)→ 2[α], and the objective is to check whether there exists a vertex subset S of cardinality at most k in G such that for all i...

We provide an alternative constructive proof of the Asymmetric Lovász Local Lemma. Our proof uses the classic algorithmic framework of Moser and the analysis introduced by Giotis, Kirousis, Psaromiligkos, and Thilikos in " On the algorithmic Lovász Local Lemma and acyclic edge coloring " , combined with the work of Bender and Richmond on the multivariable Lagrange Inversion formula.

We will define a matrix A=A1 associated with an acyclic digraph 1, such that the coefficients of the characteristic polynomial of A enumerate the paths in 1 according to their length. Our result is actually an easy consequence of a more general theorem of Goulden and Jackson, but this special case seems never to have been explicitly noted before. We will give two simple proofs, the first of whi...

The algorithm for Lovász Local Lemma by Moser and Tardos gives a constructive way to prove the existence of combinatorial objects that satisfy a system of constraints. We present an alternative probabilistic analysis of the algorithm that does not involve counting witness-trees. We then apply our approach to Acyclic Edge Coloring to obtain a direct probabilistic proof that a graph with maximum ...

A cubic graph G is uniquely edge-3-colorable if G has precisely one 1-factorization. It is proved in this paper, if a uniquely edge-3-colorable, cubic graph G is cyclically 4-edgeconnected, but not cyclically 5-edge-connected, then G must contain a snark as a minor. This is an approach to a conjecture that every triangle free uniquely edge-3-colorable cubic graph must have the Petersen graph as...

d-dimensional partial tori are graphs that can be expressed as cartesian product of d graphs each of which is an induced path or cycle. Some well known graphs like d-dimensional hypercubes, meshes and tori are examples belong to this class. Muthu et al.[MNS06] have studied the problem of acyclic edge coloring for such graphs. We try to explore the acyclic vertex coloring problem for these graph...

In this paper, we propose a novel visualization framework called DAGView. The aim of DAGView is to produce clear visualizations of directed acyclic graphs in which every edge and the potential existence of a path can be immediately spotted by the user. Several criteria that users identified as important in a layout are met, such as underlying grid, crossings and bends that appear perpendicular....

Let G be a weighted, direr.ted, acyclic graph in which each edge weight. is not a staticquantity, but can be reduced for a certain cost. In this paper we consider the problem of determining which edg('s to reduce so that the length of the longest paths is minimized and the total cost associated with the reductions does not exceed a given cost. We consider two type-s of edge reductions, linear r...

An acyclic edge coloring of a graph G is proper such that no bichromatic cycles are produced. The conjecture by Fiamčik (1978) and Alon, Sudakov Zaks (2001) states every simple with maximum degree Δ acyclically ( + 2 ) -colorable. Despite many milestones, the remains open even for planar graphs. In this paper, we confirm affirmatively on graphs without intersecting triangles. We do so first sho...