2. Main result. By an eulerian digraph we mean a digraph in which the in-degree is equal to the out-degree at each vertex. Let ED ME ( n, t) be the number of labelled loop-free eulerian digraphs with n vertices in which the multiplicity of each edge is at most t. Allowing loops would multiply ED ME (n, t) by exactly (t + 1) n, since loops do not affect the eulerian property. For the case where ...

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility—which are comparable to second and first order immobility for a single object—to capture the intuitive requirement for a fixture of a chain of hinged objects; robust immobility differs from immobility in that it additionally...

We give two combinatorial proofs of a product formula for the number of spanning trees of the n-dimensional hypercube. The first proof is based on the assertion that if one chooses a uniformly random rooted spanning tree of the hypercube and orient each edge from parent to child, then the parallel edges of the hypercube get orientations which are independent of one another. This independence pr...

We study path auction games in which multiple edges may be owned by the same agent in this paper. The edge costs and the set of edges owned by the same agent are privately known to the owner of the edges. In this setting, we show that, assuming that losing agents always have 0 payoff, there is no individual rational, strategyproof mechanism in which only edge costs are reported. If the agents a...

A c-edge-colored multigraph has each edge colored with one of the c available colors and no two parallel edges have the same color. A proper hamiltonian path is a path containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper hamiltonian path, depending on several parameter...

This paper proposes and analyzes bandwidth reclaim scheme for IEEE 802.11 WLAN, which may suffer from severe bandwidth waste resulting from not only the variation of transmission rate and message length but also the overallocation to the real-time traffic in compensating for the delay due to the intervention of non-real-time messages. Built on top of the weighted round robin scheduling policy, ...

intra-abdominal desmoplastic small round cell tumor is a rare entity with a few reports worldwide. this tumor commonly occurs in children and adolescent and occurrence in adult age group is very rare. here, we describe an adult male with symptoms of intestinal obstruction due to abdominal mass, located in splenic flexure. after resection, the diagnosis of intra-abdominal desmoplastic small roun...

Given a large graph G = (V,E) with millions of nodes and edges, how do we compute its connected components efficiently? Recent work addresses this problem in map-reduce, where a fundamental trade-off exists between the number of mapreduce rounds and the communication of each round. Denoting d the diameter of the graph, and n the number of nodes in the largest component, all prior techniques for...

We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node’s degree is split almost uniformly. Our findings lead to answers for a number of problems, a sampling of which includes: • We present a poly log n round deterministic algorithm for (2∆− 1) · (1 + o(1))-edg...