Asymptotic behavior of the number of Eulerian orientations of graphs
نویسنده
چکیده
منابع مشابه
Counting and Sampling Problems on Eulerian Graphs
In this thesis we consider two sets of combinatorial structures defined on an Eulerian graph: the Eulerian orientations and Euler tours. We are interested in the computational problems of counting (computing the number of elements in the set) and sampling (generating a random element of the set). Specifically, we are interested in the question of when there exists an efficient algorithm for cou...
متن کامل0n removable cycles in graphs and digraphs
In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...
متن کاملVertex Removable Cycles of Graphs and Digraphs
In this paper we defined the vertex removable cycle in respect of the following, if $F$ is a class of graphs(digraphs) satisfying certain property, $G in F $, the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $. The vertex removable cycles of eulerian graphs are studied. We also characterize the edge removable cycles of regular graphs(digraphs).
متن کاملOn Tensor Product of Graphs, Girth and Triangles
The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.
متن کاملThe irregularity and total irregularity of Eulerian graphs
For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.
متن کامل