Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced subgraphs, in particular for P7-free bipartite graphs. We propose a new on-line competitive coloring algorithm for P8-free bipartite graphs. Our proof technique impro...

The notion of graph powers is a well-studied topic in graph theory and its applications. In this paper, we investigate a bipartite analogue of graph powers, which we call bipartite powers of bigraphs. We show that the classes of bipartite permutation graphs and interval bigraphs are closed under taking bipartite power. We also show that the problem of recognizing bipartite powers is NP-complete...

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety o...

Example 3.1.4. Let G be a directed graph and suppose vertex v has indegree k and outdegree `, i. e., k edges end at v and ` edges start at v. Each of these k+ ` edges will represent a vertex in the directed line graph ~ L(G), and since the terminus of each of the former k edges is the initial point of each of the latter `, in the line graph each of the former will have an edge directing to each...

Abstract Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members of G share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in G are isomorphic to a given spanning subgraph G, then G is said to be an...

We analyzed simultaneous observation data with ground-based synthetic aperture radar (GB-SAR) and airborne SAR (PiSAR) over a flood test site at which a simple house was constructed in a field. The PiSAR σ◦ under flood condition was 0.9 to 3.4 dB higher than that under nonflood condition. GB-SAR gives high spatial resolution as we could identify a single scattering component and a double bounce...

The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function of N . It is shown that phase transitions of different orders occur, depending on the functional dependence of the area on N . The finite-size scalings of th...

Let r be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for r if every set in r with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on r and M): If M is a perfect set basis for r, the field of every wel...