相关论文: Are Yao Graph and Theta Graph Void Free?
A graph $G=(V,E)$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree $T$ and two non-negative real numbers $d_{min}$ and $d_{max}$, $d_{min} \leq d_{max}$, such that each node $u \in V$ is uniquely associated to a…
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is the one of the Young graded graph of integer…
Euler graphs with only one (two) type(s) of cycles under (mod 4) operation were studied in Part-I(II). Here we consider the class of Euler graphs with only three types of cycles under (mod 4). This gives rise to four cases viz., graphs…
We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right. Each packet that is forwarded arrives at the next…
The celebrated Mantel's theorem states that any triangle-free graph on $n$ vertices contains at most $\left\lfloor n^2/4\right\rfloor$ edges. It is natural to ask how many triangles must exist in a graph with more than $\left\lfloor…
Graph connectivity serves as a fundamental metric for evaluating the reliability and fault tolerance of interconnection networks. To more precisely characterize network robustness, the concept of cyclic connectivity has been introduced,…
Wireless networks are present everywhere but their management can be tricky since their coverage may contain holes even if the network is fully connected. In this paper we propose an algorithm that can build a communication tree between…
An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding $f$ of a graph $G$ into $\mathbb{R}^3$ is free, if $\pi_1(\mathbb{R}^3-f(G))$ is a free…
A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this paper, we consider (cap, even hole)-free…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
The Erd\H{o}s-Gy\'{a}rf\'{a}s conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the…
Graphical passwords (GPWs) have been studied over 20 years. We are motivated from QR codes that can be considered GPWs, are successfully applied in today's world. However, one need such GPWs that can be use conveniently and have higher…
A simple topological graph is a topological graph in which any two edges have at most one common point, which is either their common endpoint or a proper crossing. More generally, in a k-simple topological graph, every pair of edges has at…
State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.
The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for…
A subset of vertices in a graph is called a total dominating set if every vertex of the graph is adjacent to at least one vertex of this set. A total dominating set is called minimal if it does not properly contain another total dominating…
An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
Let $Z_2\times Z_2=\{0, \alpha, \beta, \alpha+\beta\}$. If $G$ is a bridgeless cubic graph, $F$ is a perfect matching of $G$ and $\overline{F}$ is the complementary 2-factor of $F$, then a no-where zero $Z_2\times Z_2$-flow $\theta$ of…