In an edge-colored graph (G,c), let dc(v) denote the number of colors on edges incident with a vertex v G and δc(G) minimum value over all vertices v∈V(G). A cycle (G,c) is called proper if any two adjacent have distinct colors. An n≥3 properly vertex-pancyclic each contained in length ℓ for every 3≤ℓ≤n. Fujita Magnant conjectured that complete δc(G)≥n+12 vertex-pancyclic. Chen, Huang Yuan part...

Xu et al. showed that for any set of faulty edges F of an n-dimensional hypercube Qn with |F | n− 1, each edge of Qn − F lies on a cycle of every even length from 6 to 2n, n 4, provided not all edges in F are incident with the same vertex. In this paper, we find that under similar condition, the number of faulty edges can be much greater and the same result still holds. More precisely, we show ...

The best worst case guarantee algorithm to see if a graph has a Hamiltonian cycle, a closed tourvisiting every vertex exactly once, for a long time was based on dynamic programming over allthe vertex subsets of the graph. In this talk we will show some algebraic techniques that can beused to see if a graph has a Hamiltonian cycle much faster. These techniques utilize sums over<l...

We give a simple geometric interpretation of an algebraic construction Wenger that gives n-vertex graphs with no cycle length 4, 6, or 10 and close to the maximum number edges.

OBJECTIVE To investigate the relationship between removable dentures and swallowing and describe risks. METHODS Twenty-four patients with removable dentures who were referred for videofluoroscopic swallowing study (VFSS) were enrolled. We evaluated the change of swallowing function using VFSS before and after the removal of the removable denture. The masticatory performance by Kazunori's meth...

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph Γ, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of Γ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular...

A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a simple and efficient approximation algorithm with performance ratio of at most 2, improving previous best bounds for either weighted or unweighted case...

A 4-wheel is a simple graph on 5 vertices with 8 edges, consisting of a 4-cycle, with a fifth vertex joined to each vertex in the 4-cycle. A A-fold 4-wheel system of order n is an edge-disjoint decomposition of AKn into 4-wheels. If two non-adjacent edges of the 4-cycle are removed, the result is a bowtie (that is, two triangles with a common vertex). In this paper necessary and sufficient cond...

In wireless multihop networks, the objective of the broadcast scheduling problem is to find a conflict free transmission schedule for each node at different time slots in a fixed length time cycle, called TDMA cycle. The optimization criterion is to find an optimal TDMA schedule with minimal TDMA cycle length and maximal node transmissions. In this paper we propose a two-stage hybrid method to ...

A wheel is an induced cycle C plus a vertex connected to at least three vertices of C. Trotignon [14] asked if the class of wheel-free graphs is χ-bounded, i.e. if the chromatic number of every graph with no induced copy of a wheel is bounded by a function of its maximal clique. In this paper, we prove a weaker statement: for every `, the class of graphs with no induced wheel and no induced K`,...