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1
Content available Race and Horror in HBO’s Lovecraft Country
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This article is an analysis of the HBO series Lovecraft Country in terms of the elements of racism and traditional horror elements present in it, including elements typical of the prose of one of the genre’s creators, H. P. Lovecraft. The purpose of the article is to explore typical horror elements that appear in the series and show how the authors of the series combine traditional horror with the horror of everyday life in the oppressed Black community in 1950s America. At the beginning of the article, the series and its main idea are described. The article then takes up the subject of the portrayal of racism in the series, specific examples of which are presented and discussed in terms of their compatibility with the realities of America at the time. The article also discusses elements related to the antiracism movement – situations presented in the series that exemplify the character’ struggle against racism are shown. Then the otherness depicted in the series is discussed – not only racial otherness, but also gender and sexual otherness; in this part of the article, otherness is given as a reason for oppression by society. The article also explores the use of traditional elements of horror genre in the series – it indicates which scenes in the series use the traditional concepts of the horror genre, and attempts to show which characters in the series function as monsters in the story. At the end of the article, it is explained how the series draws inspiration in the works of Lovecraft, whose name appears in the very title of the series.
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Content available On cyclically embeddable graphs
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An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.
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Content available A note on uniquely embeddable graphs
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Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an embedding G into its complement [G̅]. In this note, we consider a problem concerning the uniqueness of such an embedding.
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Content available remote A Note on Uniquely Embeddable Forests
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Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.
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For a graph G of order n we consider the unique partition of its vertex set V(G) = A ∪ B with A = {v ∈ V(G): d(v) ≥ n/2} and B = {v ∈ V(G):d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.
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Content available A note on packing of two copies of a hypergraph
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A 2-packing of a hypergraph 𝓗 is a permutation σ on V(𝓗) such that if an edge e belongs to 𝓔(𝓗), then σ (e) does not belong to 𝓔(𝓗). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(𝓗) and has at most 1/2n edges is 2-packable. A 1-uniform hypergraph of order n with more than 1/2n edges shows that this result cannot be improved by increasing the size of 𝓗.
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Content available remote Rainbow Connection In Sparse Graphs
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An edge-coloured connected graph G = (V,E) is called rainbow-connected if each pair of distinct vertices of G is connected by a path whose edges have distinct colours. The rainbow connection number of G, denoted by rc(G), is the minimum number of colours such that G is rainbow-connected. In this paper we prove that rc(G) ≤ k if |V (G)| = n and for all integers n and k with n − 6 ≤ k ≤ n − 3. We also show that this bound is tight.
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Content available remote Dense Arbitrarily Partitionable Graphs
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A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . . , Vk) of the vertex set V (G) such that Vi induces a connected subgraph of order ni for i = 1, . . . , k. In this paper we show that every connected graph G of order n ≥ 22 and with [...] ‖G‖ > (n−42)+12 $||G||\; > \;\left( {\matrix{{n - 4} \cr 2 \cr } } \right) + 12$ edges is AP or belongs to few classes of exceptional graphs.
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Content available A note on a new condition implying pancyclism
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We first show that if a 2-connected graph G of order n is such that for each two vertices u and v such that δ = d(u) and d(v) < n/2 the edge uv belongs to E(G), then G is hamiltonian. Next, by using this result, we prove that a graph G satysfying the above condition is either pancyclic or isomorphic to $K_{n/2,n/2}$.
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Content available On cyclically embeddable (n,n)-graphs
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An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.
EN
Let 𝓕 ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set 𝓕 ⁿ is a common subgraph F of order n of each member of 𝓕 ⁿ, that is not properly contained in any larger common subgraph of each member of 𝓕 ⁿ. By well-known Dirac's Theorem, the Dirac's family 𝓓𝓕 ⁿ of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cₙ. In this note we study the problem of determining all maximal common subgraphs of the Dirac's family $𝓓 𝓕 ^{2n}$ for n ≥ 2.
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Content available remote A Note on Neighbor Expanded Sum Distinguishing Index
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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
EN
Aim: Respiratory syncytial virus is the main pathogen responsible for bronchiolitis. Usually, there is no indication to perform diagnostic imaging or run laboratory tests in patients with bronchiolitis since the diagnosis is based on the clinical presentation. Chest radiogram can be useful in severe cases. So far, lung ultrasound has not been considered as an alternative in guidelines for imaging diagnosis of bronchiolitis. The aim of the study was to compare lung ultrasound and chest X-ray findings in children with bronchiolitis. Material and methods: In our study we retrospectively compared diagnostic imaging findings in children with confirmed respiratory syncytial virus infection. The study included 23 children aged 2 weeks to 24 months and 3 children older than 24 months. Results: Chest X-ray showed lesions in only 4 cases, whereas ultrasound abnormalities were found in 21 patients. Pathologies revealed by chest Xray were the same for all 4 cases and consisted of an enlarged hilus and peribronchial cuffing. Sonographic lesions included inflammatory consolidations larger than 10 mm in 11 patients, small consolidations (<10 mm diameter) in 8 patients, interstitial syndromes in 6 patients, and alveolar-interstitial syndromes in 11 patients. A small amount of pleural effusion was detected in 3 patients. Conclusions: Considering safety, short time of examination, high sensitivity in finding pleural effusion, small consolidations and signs of interstitial infiltrations, transthoracic lung ultrasound may be useful in the diagnosis of bronchiolitis.
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Cel badania: Wirus respiratory syncytial jest głównym patogenem powodującym ostre zapalenie oskrzelików. Zwykle u pacjentów z zapaleniem oskrzelików nie ma wskazań do wykonywania badań obrazowych i laboratoryjnych, a rozpoznanie opiera się na obrazie klinicznym. W cięższych przypadkach przydatne może być badanie rentgenowskie klatki piersiowej. Dotychczas nie uwzględniono badania ultrasonograficznego płuc w wytycznych dotyczących diagnostyki tego schorzenia. W naszej pracy porównaliśmy wyniki badań obrazowych: ultrasonograficznych płuc i rentgenowskich klatki piersiowej u dzieci z zapaleniem oskrzelików. Materiały i metody: Retrospektywnie porównano wyniki przezklatkowego badania ultrasonograficznego płuc i zdjęcia rentgenowskie klatki piersiowej u dzieci z potwierdzonym zakażeniem respiratory syncytial virus. Do badania włączono 23 dzieci w wieku od 2 tygodni do 24 miesięcy i 3 dzieci w wieku powyżej 24 miesięcy. Wyniki: Zmiany patologiczne w badaniu rentgenowskim klatki piersiowej uwidoczniono w czterech przypadkach, podczas gdy w badaniu ultrasonograficznym zmiany stwierdzono u 21 pacjentów. Na zdjęciu rentgenowskim klatki piersiowej u wszystkich czterech pacjentów opisano poszerzenie wnęk i zagęszczenia okołooskrzelowe. Zmiany stwierdzone w obrazie ultrasonograficznym obejmowały: konsolidacje zapalne większe niż 10 mm u 11 pacjentów, małe konsolidacje (<10 mm średnicy) u 8 pacjentów, zespoły śródmiąższowe u 6 pacjentów, zespoły śródmiąższowo-pęcherzykowe u 11 pacjentów. W 3 przypadkach stwierdzono niewielką ilość płynu wysiękowego w opłucnej. Wnioski: Z uwagi na bezpieczeństwo, krótki czas badania oraz wysoką czułość w obrazowaniu wysięku opłucnowego, małych konsolidacji i zmian śródmiąższowych przezklatkowe badanie ultrasonograficzne płuc może być użyteczne w diagnostyce zapalenia oskrzelików.
EN
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,aₖ) of positive integers such that a₁+...+aₖ = n there exists a partition (V₁,...,Vₖ) of the vertex set of G such that for each i ∈ {1,...,k}, $V_i$ induces a connected subgraph of G on $a_i$ vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable caterpillars with four leaves. We also describe two families of arbitrarily vertex decomposable trees with maximum degree three or four.
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Content available Chvátal-Erdos condition and pancyclism
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The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result can be easily proved by applying only classical Ramsey numbers.
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