Results 51 to 60 of about 169,932 (295)
Generalized Rainbow Connection of Graphs and their Complements
Discussiones Mathematicae Graph Theory, 2018 Let G be an edge-colored connected graph. A path P in G is called ℓ-rainbow if each subpath of length at most ℓ + 1 is rainbow. The graph G is called (k, ℓ)-rainbow connected if there is an edge-coloring such that every pair of distinct vertices of G is ...
Li Xueliang +3 more
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Teaching Combinatorial Principles Using Relations through the Placemat Method
Mathematics, 2021 The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific ...
Viliam Ďuriš +3 more
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Simple 3‐Designs of PSL ( 2 , 2 n ) With Block Size 13
Journal of Combinatorial Designs, EarlyView.ABSTRACT This paper focuses on the investigation of simple 3‐ ( 2 n + 1 , 13 , λ ) designs admitting PSL ( 2 , 2 n ) as an automorphism group. Such designs arise from the orbits of 13‐element subsets under the action of PSL ( 2 , 2 n ) on the projective line X = GF ( 2 n ) ∪ { ∞ }, and any union of these orbits also forms a 3‐design.
Takara Kondo, Yuto Nogata
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Hodge theory in combinatorics [PDF]
, 2017 George Birkhoff proved in 1912 that the number of proper colorings of a finite graph G with n colors is a polynomial in n, called the chromatic polynomial of G.
M. Baker
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Recursive and Cyclic Constructions for Double‐Change Covering Designs
Journal of Combinatorial Designs, EarlyView.ABSTRACT A double‐change covering design (DCCD) is a v $v$‐set V $V$ and an ordered list L ${\mathscr{L}}$ of b $b$ blocks of size k $k$ where every pair from V $V$ must occur in at least one block and each pair of consecutive blocks differs by exactly two elements. It is minimal if it has the fewest blocks possible and circular when the first and last
Amanda Lynn Chafee, Brett Stevens
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Combinatorics of embeddings [PDF]
, 2011 We offer the following explanation of the statement of the Kuratowski graph planarity criterion and of 6/7 of the statement of the Robertson-Seymour-Thomas intrinsic linking criterion.
Melikhov, Sergey A.
core
On the Rainbow Vertex-Connection
Discussiones Mathematicae Graph Theory, 2013 A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph G, denoted by rvc(G), is the smallest number of colors that ...
Li Xueliang, Shi Yongtang
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Subsquares in Random Latin Squares and Rectangles
Journal of Combinatorial Designs, EarlyView.ABSTRACT A k×n $k\times n$ partial Latin rectangle is C‐sparse $C \mbox{-} \mathrm{sparse}$ if the number of nonempty entries in each row and column is at most C $C$ and each symbol is used at most C $C$ times. We prove that the probability a uniformly random k×n $k\times n$ Latin rectangle, where k<(1∕2−α)n $k\lt (1\unicode{x02215}2-\alpha )n ...
Alexander Divoux +3 more
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Hopf Algebras in Combinatorics
, 2020 These notes -- originating from a one-semester class by their second author at the University of Minnesota -- survey some of the most important Hopf algebras appearing in combinatorics.
Grinberg, Darij, Reiner, Victor
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A note on global existence for boundary value problems
International Journal of Mathematics and Mathematical Sciences, 1989 Upper and lower solutions are used in establlsning global existence results for certain two–point boundary value problems for y‴=f(x,y,y′,y″) and y(n)=f(x,y,y′,...,y(n−1)).
Chuan J. Chyan, Johnny Henderson
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