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Let k be a positive integer. A graph G is k -matching-connected if G − V ( M ) is connected and nontrivial, for each matching M of G with | M | ≤ k − 1. For a k-matching-connected graph G, an edge e ∉ E ( G ) is said to be addible if G + e is ...

In this paper we consider the seating couples problem with an even number of seats, which, using graph theory terminology, can be stated as follows. Given a positive even integer v = 2 n and a list L containing n positive integers not exceeding n,...

We initiate the study of fairness among classes of agents in online bipartite matching where there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online and must be matched irrevocably upon ...

Learning feature correspondence is a foundational task in computer vision, holding immense importance for downstream applications such as visual odometry and 3D reconstruction. Despite recent progress in data-driven models, feature correspondence ...

Let m ( H , t ) be the number of matchings containing t edges in a graph H. Define a quasi-order ⪰ by H ⪰ F if m ( H , t ) ≥ m ( F , t ) holds for all t. Let B C ( a , b , r ) be the set of all bipartite cacti with r cycles and a given ...

• The graphs minimize the matching energy in a given graph class are determined.
• Develop some graph operations for comparing the matching energies of two graphs.
• Use recursion idea to count the number of matchings with fixed size in ...

We consider one-sided matching problems, where agents are allocated items based on stated preferences. Posing this as an assignment problem, the average rank of obtained matchings can be minimized using the rank minimization (RM) mechanism. RM ...

Let $G=(V,E)$ be an undirected complete graph on kn vertices. Each edge is associated with a non-negative weight. The edge weights satisfies the triangle inequality. A k-cycle partitioning is a set of n vertex-disjoint k-cycles, i.e. cycles ...$\mathrm{}$

The 2-Decomposition Conjecture, equivalent to the 3-Decomposition Conjecture stated in 2011 by Hoffmann-Ostenhof, claims that every connected graph G with vertices of degree 2 and 3, for which $G\backslash E(C)$ is disconnected for every cycle C, admits a ...

Let $\beta >0$. Motivated by the notion of jumbled graphs introduced by Thomason, the expander mixing lemma and Haemers’s vertex separation inequality, we say that a graph G with n vertices is a weakly $(n,\beta )$-graph if $\frac{|X||Y|}{(n-|X|)(n-|Y|)}\le {\beta }^2$ holds for ...$$$$$$$$$$$$$$$\frac{{}_{}{}_{\mathrm{}}}{{}_{}{}_{\mathrm{}}}$${}_{}$$$$$$$${}^{}\left\{\frac{\mathrm{}}{\mathrm{}},,,\frac{\mathrm{}}{\mathrm{}}\right\}\mathrm{}$$$$\mathrm{}$${}^{}\mathrm{}\mathrm{}{}^{\mathrm{}}\mathrm{}$$$${}^{}\left\{\frac{\mathrm{}}{\mathrm{}\mathrm{}},,,\frac{\mathrm{}}{\mathrm{}}\right\}\mathrm{}$$$${}^{}\mathrm{}{}^{\mathrm{}}\mathrm{}$$$$\mathrm{}\mathrm{}\mathrm{}$$$$\mathrm{}\mathrm{}\mathrm{}$$$$\frac{\mathrm{}}{}$$$$\frac{\mathrm{}\mathrm{}}{\mathrm{}}$$\left(\frac{\mathrm{}}{\mathrm{}},,\right)\frac{\mathrm{}}{}$$\mathrm{}$

Multi-access edge computing (MEC), as a computing model that provides services on the user side, can effectively solve the problems of high delay and resource shortage in traditional cloud computing when processing massive data. However, existing ...

The paper presents 3D ear recognition which is based on the coherent point drift (CPD) algorithm. It primarily does the tasks of rigid point set registration followed by EM (expectation maximization) optimization. Automatic detection of pit points ...

Let α = a 1 a 2 … a n be a sequence of nonnegative integers. The ascent set of α, Asc α, consists of all indices k where a k + 1 > a k. An ascent sequence is α where the growth of the a k is bounded by the elements of Asc α. These sequences were ...

Group encryption (GE), introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), is the encryption analogue of group signatures. It allows to send verifiably encrypted messages satisfying certain requirements to certified members of a group, while ...

This paper presents a novel approach to support career management by recommending job–employee matches within an organization through data-driven insights. We build a recommender system to propose matches. The presented approach extends upon a ...

The classic theorem of Vizing (Diskret. Analiz.’64) asserts that any graph of maximum degree Δ can be edge colored (offline) using no more than Δ+1 colors (with Δ being a trivial lower bound). In the online setting, Bar-Noy, Motwani and Naor (IPL’92) ...

We design an additive approximation scheme for estimating the cost of the min-weight bipartite matching problem: given a bipartite graph with non-negative edge costs and ε > 0, our algorithm estimates the cost of matching all but O(ε)-fraction of the ...

This paper studies three edge-removing games on graphs. In each game, there are two players and a simple graph G at the beginning. The players take turns removing at least one edge of a certain type from the current graph. The one who cannot move ...

3D reconstruction can be used to satisfy the increasing requirement of people to 3D images and 3D videos with naked eye or not. With the development of deep learning, more and more attention to deep learning applications in the field of three-dimensional ...

Let s , m , n be positive integers and F be a graph. A graph G is called F-saturated if F is not a subgraph of G but G + e contain a copy of F for every edge e ∈ E ( G ¯ ), where G ¯ is the complement graph of G. Let s a t ( n , F ) be the ...

Blockchain received a vast amount of attention in recent years and is still growing. The second generation of blockchain, such as Ethereum, allows execution of almost any program in EVM, making it a global protocol for distributed applications. ...