General neighbour-distinguishing index via chromatic number

AbstractAn edge colouring of a graph G without isolated edges is neighbour-distinguishing if any two adjacent vertices have distinct sets consisting of colours of their incident edges. The general neighbour-distinguishing index of G is the minimum number gndi(G) of colours in a neighbour-distinguishing edge colouring of G. Győri et al. [E. Győri, M. Horňák, C. Palmer, M. Woźniak, General neighbour-distinguishing index of a graph, Discrete Math. 308 (2008) 827–831] proved that gndi(G)∈{2,3} provided G is bipartite and gave a complete characterisation of bipartite graphs according to their general neighbour-distinguishing index. The aim of this paper is to prove that if χ(G)≥3, then ⌈log2χ(G)⌉+1≤gndi(G)≤⌊log2χ(G)⌋+2. Therefore, if log2χ(G)∉Z, then gndi(G)=⌈log2χ(G)⌉+1

Total edge irregularity strength of complete graphs and complete bipartite graphs

AbstractA total edge irregular k-labelling ν of a graph G is a labelling of the vertices and edges of G with labels from the set {1,…,k} in such a way that for any two different edges e and f their weights φ(f) and φ(e) are distinct. Here, the weight of an edge g=uv is φ(g)=ν(g)+ν(u)+ν(v), i. e. the sum of the label of g and the labels of vertices u and v. The minimum k for which the graph G has an edge irregular total k-labelling is called the total edge irregularity strength of G.We have determined the exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs

Úloha črevných cirkadiánnych hodín v epiteliálnom transporte, proliferácii a tumorigenéze.

AABBSSTTRRAAKKTT Molekulárne cirkadiánne hodiny umožňujú predvídanie zmien v okolitom prostredí. U cicavcov sú molekulárne hodiny prítomné prakticky vo všetkých tkanivách a tvorí ich sústava transkripčno-translačných spätnoväzbových slučiek tzv. hodinových génov. Centrálne hodiny predstavujú vnútorný pacemaker, ktorý sa nachádza v suprachiazmatických jadrách (SCN) hypotalamu a synchronizuje periférne hodiny. Cirkadiánne hodiny v tráviacom trakte a ich podiel na regulácii črevných funkcií sú nedostatočne preskúmané. Preto bolo cieľom tejto práce charakterizovať molekulárne hodiny v jednotlivých častiach čreva potkana a objasniť ich úlohu v regulácii epiteliálneho transportu, bunkového cyklu a nádorovej transformácie v hrubom čreve. Na stanovenie cirkadiánnych profilov expresie hodinových génov v epiteli duodena, jejuna, ilea a hrubého čreva potkana sme použili kvantitatívnu RT-PCR (qPCR). Ďalej sme analyzovali expresiu génov kódujúcich transportéry a kanály umožňujúcich transport NaCl, ako aj regulátorov bunkového cyklu v hrubom čreve. Na detailnejší popis expresie v rámci štruktúr črevného epitelu sme použili laserovú mikrodisekciu. Elektrogénny transepiteliálny transport bol meraný ako skratovací prúd v Ussingových komorách. Na určenie úlohy hodín v procese tumorigenézy sme použili myší model azoxymetánom...AABBSSTTRRAACCTT The molecular circadian clock enables anticipation of environmental changes. In mammals, clocks are ubiquitously present in almost all tissues and they are comprised of transcriptional-translational feedback loops of the so-called clock genes. The central clock represents the intrinsic pacemaker which is located in suprachiasmatic nuclei (SCN) of hypothalamus and synchronizes peripheral clocks. Clockwork system in alimentary tract and its regulatory link to intestinal functions are poorly understood. Therefore the objective of the thesis was to characterize molecular clock in particular parts of the rat intestine and to elucidate its link to the intestinal transport, regulation of cell cycle and neoplastic transformation in colonic tissue. We used quantitative RT-PCR (qPCR) to determine circadian profiles of mRNA expression of clock genes in the epithelium of duodenum, jejunum, ileum, and colon of rat. Furthermore, we analysed the expression of genes coding sodium chloride transporters and channels as well as cell cycle regulators in colon. To focus more precisely on different structures of intestinal epithelia we used laser capture microdissection. In addition, we performed Ussing chamber measurements to determine the colonic electrogenic transport. To study the contribution of circadian...Katedra fyziologieDepartment of PhysiologyFaculty of SciencePřírodovědecká fakult

A note on vertex colorings of plane graphs

Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V , let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) 6= c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2

Úloha črevných cirkadiánnych hodín v epiteliálnom transporte, proliferácii a tumorigenéze.

AABBSSTTRRAACCTT The molecular circadian clock enables anticipation of environmental changes. In mammals, clocks are ubiquitously present in almost all tissues and they are comprised of transcriptional-translational feedback loops of the so-called clock genes. The central clock represents the intrinsic pacemaker which is located in suprachiasmatic nuclei (SCN) of hypothalamus and synchronizes peripheral clocks. Clockwork system in alimentary tract and its regulatory link to intestinal functions are poorly understood. Therefore the objective of the thesis was to characterize molecular clock in particular parts of the rat intestine and to elucidate its link to the intestinal transport, regulation of cell cycle and neoplastic transformation in colonic tissue. We used quantitative RT-PCR (qPCR) to determine circadian profiles of mRNA expression of clock genes in the epithelium of duodenum, jejunum, ileum, and colon of rat. Furthermore, we analysed the expression of genes coding sodium chloride transporters and channels as well as cell cycle regulators in colon. To focus more precisely on different structures of intestinal epithelia we used laser capture microdissection. In addition, we performed Ussing chamber measurements to determine the colonic electrogenic transport. To study the contribution of circadian...AABBSSTTRRAAKKTT Molekulárne cirkadiánne hodiny umožňujú predvídanie zmien v okolitom prostredí. U cicavcov sú molekulárne hodiny prítomné prakticky vo všetkých tkanivách a tvorí ich sústava transkripčno-translačných spätnoväzbových slučiek tzv. hodinových génov. Centrálne hodiny predstavujú vnútorný pacemaker, ktorý sa nachádza v suprachiazmatických jadrách (SCN) hypotalamu a synchronizuje periférne hodiny. Cirkadiánne hodiny v tráviacom trakte a ich podiel na regulácii črevných funkcií sú nedostatočne preskúmané. Preto bolo cieľom tejto práce charakterizovať molekulárne hodiny v jednotlivých častiach čreva potkana a objasniť ich úlohu v regulácii epiteliálneho transportu, bunkového cyklu a nádorovej transformácie v hrubom čreve. Na stanovenie cirkadiánnych profilov expresie hodinových génov v epiteli duodena, jejuna, ilea a hrubého čreva potkana sme použili kvantitatívnu RT-PCR (qPCR). Ďalej sme analyzovali expresiu génov kódujúcich transportéry a kanály umožňujúcich transport NaCl, ako aj regulátorov bunkového cyklu v hrubom čreve. Na detailnejší popis expresie v rámci štruktúr črevného epitelu sme použili laserovú mikrodisekciu. Elektrogénny transepiteliálny transport bol meraný ako skratovací prúd v Ussingových komorách. Na určenie úlohy hodín v procese tumorigenézy sme použili myší model azoxymetánom...Department of PhysiologyKatedra fyziologieFaculty of SciencePřírodovědecká fakult