Displaying similar documents to “A note on perfect matchings in uniform hypergraphs with large minimum collective degree”

The sum number of d-partite complete hypergraphs

Hanns-Martin Teichert (1999)

Discussiones Mathematicae Graph Theory

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A d-uniform hypergraph is a sum hypergraph iff there is a finite S ⊆ IN⁺ such that is isomorphic to the hypergraph d ( S ) = ( V , ) , where V = S and = v , . . . , v d : ( i j v i v j ) i = 1 d v i S . For an arbitrary d-uniform hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices w , . . . , w σ V such that w , . . . , w σ is a sum hypergraph. In this paper, we prove σ ( n , . . . , n d d ) = 1 + i = 1 d ( n i - 1 ) + m i n 0 , 1 / 2 ( i = 1 d - 1 ( n i - 1 ) - n d ) , where n , . . . , n d d denotes the d-partite complete hypergraph; this generalizes the corresponding result of Hartsfield and Smyth [8] for complete bipartite graphs.

Sum labellings of cycle hypergraphs

Hanns-Martin Teichert (2000)

Discussiones Mathematicae Graph Theory

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A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph d ̲ , [ d ̅ ] ( S ) = ( V , ) where V = S and = e S : d ̲ | e | [ d ̅ ] v e v S . For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices y , . . . , y σ V such that y , . . . , y σ is a sum hypergraph. Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings...

Classes of hypergraphs with sum number one

Hanns-Martin Teichert (2000)

Discussiones Mathematicae Graph Theory

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A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ with 1 < d̲ < d̅ such that ℋ is isomorphic to the hypergraph d ̲ , d ̅ ( S ) = ( V , ) where V = S and = e S : d ̲ < | e | < d ̅ v e v S . For an arbitrary hypergraph ℋ the sum number(ℋ ) is defined to be the minimum number of isolatedvertices w , . . . , w σ V such that w , . . . , w σ is a sum hypergraph. For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs ₙ and ₙ that under a certain condition...

Bounds for the number of meeting edges in graph partitioning

Qinghou Zeng, Jianfeng Hou (2017)

Czechoslovak Mathematical Journal

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Let G be a weighted hypergraph with edges of size at most 2. Bollobás and Scott conjectured that G admits a bipartition such that each vertex class meets edges of total weight at least ( w 1 - Δ 1 ) / 2 + 2 w 2 / 3 , where w i is the total weight of edges of size i and Δ 1 is the maximum weight of an edge of size 1. In this paper, for positive integer weighted hypergraph G (i.e., multi-hypergraph), we show that there exists a bipartition of G such that each vertex class meets edges of total weight at least ( w 0 - 1 ) / 6 + ( w 1 - Δ 1 ) / 3 + 2 w 2 / 3 , where...

Monotonically normal e -separable spaces may not be perfect

John E. Porter (2018)

Commentationes Mathematicae Universitatis Carolinae

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A topological space X is said to be e -separable if X has a σ -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that e -separable PIGO spaces are perfect and asked if e -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of e -separable monotonically normal spaces which are not perfect. Extremely normal e -separable spaces are shown to be stratifiable.

Fires on trees

Jean Bertoin (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider random dynamics on the edges of a uniform Cayley tree with n vertices, in which edges are either flammable, fireproof, or burnt. Every flammable edge is replaced by a fireproof edge at unit rate, while fires start at smaller rate n - α on each flammable edge, then propagate through the neighboring flammable edges and are only stopped at fireproof edges. A vertex is called fireproof when all its adjacent edges are fireproof. We show that as n , the terminal density of fireproof...

On g c -colorings of nearly bipartite graphs

Yuzhuo Zhang, Xia Zhang (2018)

Czechoslovak Mathematical Journal

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Let G be a simple graph, let d ( v ) denote the degree of a vertex v and let g be a nonnegative integer function on V ( G ) with 0 g ( v ) d ( v ) for each vertex v V ( G ) . A g c -coloring of G is an edge coloring such that for each vertex v V ( G ) and each color c , there are at least g ( v ) edges colored c incident with v . The g c -chromatic index of G , denoted by χ g c ' ( G ) , is the maximum number of colors such that a g c -coloring of G exists. Any simple graph G has the g c -chromatic index equal to δ g ( G ) or δ g ( G ) - 1 , where δ g ( G ) = min v V ( G ) d ( v ) / g ( v ) . A graph G is nearly bipartite,...

Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles

Donghan Zhang (2022)

Czechoslovak Mathematical Journal

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Let G = ( V ( G ) , E ( G ) ) be a simple graph and E G ( v ) denote the set of edges incident with a vertex v . A neighbor sum distinguishing (NSD) total coloring φ of G is a proper total coloring of G such that z E G ( u ) { u } φ ( z ) z E G ( v ) { v } φ ( z ) for each edge u v E ( G ) . Pilśniak and Woźniak asserted in 2015 that each graph with maximum degree Δ admits an NSD total ( Δ + 3 ) -coloring. We prove that the list version of this conjecture holds for any IC-planar graph with Δ 11 but without 5 -cycles by applying the Combinatorial Nullstellensatz.

On decomposability of finite groups

Ruifang Chen, Xianhe Zhao (2017)

Czechoslovak Mathematical Journal

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Let G be a finite group. A normal subgroup N of G is a union of several G -conjugacy classes, and it is called n -decomposable in G if it is a union of n distinct G -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained...

Even factor of bridgeless graphs containing two specified edges

Nastaran Haghparast, Dariush Kiani (2018)

Czechoslovak Mathematical Journal

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An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let G be a bridgeless simple graph with minimum degree at least 3 . Jackson and Yoshimoto (2007) showed that G has an even factor containing two arbitrary prescribed edges. They also proved that G has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges e 1 and e 2 of G , there is an even factor containing e 1 and e 2 ...

Color-bounded hypergraphs, V: host graphs and subdivisions

Csilla Bujtás, Zsolt Tuza, Vitaly Voloshin (2011)

Discussiones Mathematicae Graph Theory

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A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set = E₁,...,Eₘ, together with integers s i and t i satisfying 1 s i t i | E i | for each i = 1,...,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge E i satisfies s i | φ ( E i ) | t i . The hypergraph ℋ is colorable if it admits at least one proper coloring. We consider hypergraphs ℋ over a “host graph”, that means a graph G on the same vertex set X as ℋ, such that each E i induces a connected subgraph in G....

Distance independence in graphs

J. Louis Sewell, Peter J. Slater (2011)

Discussiones Mathematicae Graph Theory

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For a set D of positive integers, we define a vertex set S ⊆ V(G) to be D-independent if u, v ∈ S implies the distance d(u,v) ∉ D. The D-independence number β D ( G ) is the maximum cardinality of a D-independent set. In particular, the independence number β ( G ) = β 1 ( G ) . Along with general results we consider, in particular, the odd-independence number β O D D ( G ) where ODD = 1,3,5,....