RESULTS AND OPEN PROBLEMS IN MATCHINGS IN REGULAR ...

Results and open problems in matchings in regular graphs - arXiv

Title:Results and open problems in matchings in regular graphs ... Abstract:This survey paper deals with upper and lower bounds on the number of k ...

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Results and open problems in matchings in regular graphs

Results and open problems in matchings in regular graphs ... Make a Submission. Make a Submission. Electronic Journal of Linear Algebra. A publication of the ...

Results and open problems in matchings in regular graphs

This survey paper deals with upper and lower bounds on the number of $k$-matchings in regular graphs on $N$ vertices. For the upper bounds we recall the ...

RESULTS AND OPEN PROBLEMS IN MATCHINGS IN REGULAR ...

Abstract. This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall ...

Nearly perfect matchings in regular simple hypergraphs

Our main result is the following stronger result. Theorem 1.1 Let (V,H) be a simple k-uniform, D-regular hypergraph on N vertices. If k > 3 there.

Matchings and Independent Sets: Problems, Conjectures and Results

Exact matching bounds for 2-regular graphs. 4. LMC for regular graphs. 5 ... Open even for k = n. Known for d = 2 Friedland-Krop-Markstr¨om. 5. Page 6. 5 ...

Counting and Sampling Perfect Matchings in Regular Expanding ...

... open problems in the field of counting. Jerrum and Sinclair in their landmark result [JS89] designed a Monte Carlo Markov Chain (MCMC).

Random perfect matchings in regular graphs - Wiley Online Library

A remarkable result due to Kahn and Kim 6 says that in any -regular graph , the probability that a vertex is contained in a uniformly chosen ...

Counting and Sampling Perfect Matchings in Regular Expanding ...

... problem of counting the number of perfect matchings in 𝐺 is one of the most fundamental open problems in the field of counting. Jerrum and ...

Properly Coloured Cycles and Paths: Results and Open Problems

In particular, we consider a family of transformations of an edge-coloured multigraph. G into an ordinary graph that allow us to check the existence of PC.

Some open problems in matchings in graphs

E(det(√tI + Y(B)) = ΦGw (t) - the weighted matching polynomial of. G(A). All the results for bipartite graphs carry over to nonbipatite graphs.

Bridgeless 4-Regular Graphs And Their Perfect Matchings

... challenges, with significant implications for both theoretical and practical applications in graph theory. Sources and full results. Most relevant research ...

The exclusive popular set problem asks if there is a popular matching in the given bipartite graph where the set of matched vertices is S, for a ...

Matching Problem - an overview | ScienceDirect Topics

Kalyanasundaram and Pruhs [233] survey on-line versions of standard network optimization problems. ... results can now be improved: Open problem 29. Does the ...

Regular graphs with equal matching number and independence ...

They also proposed the following two open problems. Problem 3 (Caro ... Pepper, New results relating independence and matchings, https ...

Open problems | Louis Esperet

... matchings modulo 3 in random cubic bipartite graphs (2022) # In this paper I ... regular bipartite graph has a number of perfect matching that is ...

2.7 Matching in Bipartite Graphs

Draw as many fundamentally different examples of bipartite graphs that do NOT have matchings. Your goal is to find all the possible obstructions to a graph ...

Regular expressions: new results and open problems

Regular expressions have been studied for nearly 50 years, yet many intriguing problems about their descriptive capabilities remain open.

Open problems in the spectral theory of signed graphs

where n is the number of vertices of Γ. Heilmann and Lieb [49] proved the following results regarding the matching polynomial of a graph. See ...