73 research outputs found
On deficiency problems for graphs
Motivated by analogous questions in the setting of Steiner triple systems and
Latin squares, Nenadov, Sudakov and Wagner [Completion and deficiency problems,
Journal of Combinatorial Theory Series B, 2020] recently introduced the notion
of graph deficiency. Given a global spanning property and a graph
, the deficiency of the graph with respect to the
property is the smallest non-negative integer such that the
join has property . In particular, Nenadov, Sudakov and
Wagner raised the question of determining how many edges an -vertex graph
needs to ensure contains a -factor (for any fixed ).
In this paper we resolve their problem fully. We also give an analogous result
which forces to contain any fixed bipartite -vertex graph of
bounded degree and small bandwidth.Comment: 11 page
The induced saturation problem for posets
For a fixed poset , a family of subsets of is induced
-saturated if does not contain an induced copy of , but for
every subset of such that , then is an
induced subposet of . The size of the smallest such
family is denoted by . Keszegh, Lemons,
Martin, P\'alv\"olgyi and Patk\'os [Journal of Combinatorial Theory Series A,
2021] proved that there is a dichotomy of behaviour for this parameter: given
any poset , either or . In this paper we improve this general result showing that either
or . Our proof
makes use of a Tur\'an-type result for digraphs.
Curiously, it remains open as to whether our result is essentially best
possible or not. On the one hand, a conjecture of Ivan states that for the
so-called diamond poset we have ; so if true this conjecture implies our result is tight up to a
multiplicative constant. On the other hand, a conjecture of Keszegh, Lemons,
Martin, P\'alv\"olgyi and Patk\'os states that given any poset , either
or . We prove that this
latter conjecture is true for a certain class of posets .Comment: 12 page
A general bound for the induced poset saturation problem
For a fixed poset P, a family F of subsets of [n] is induced P-saturated if F does not contain an induced copy of P, but for every subset S of [n] such that S ∉ F, then P is an induced subposet of F ∪ {S}. The size of the smallest such family F is denoted by sat* (n, P). Keszegh, Lemons, Martin, Pálvölgyi and Patkós [Journal of Combinatorial Theory Series A, 2021] proved that there is a dichotomy of behaviour for this parameter: given any poset P, either sat* (n, P) = O(1) or sat* (n, P) ≥ log2n. We improve this general result showing that either sat* (n, P) = O(1) or sat* (n, P) ≥ 2√n-2. Our proof makes use of a Turán-type result for digraphs. Curiously, it remains open as to whether our result is essentially best possible or not. On the one hand, a conjecture of Ivan states that for the so-called diamond poset ◊ we have sat* (n, ◊) = Θ(√n); so if true this conjecture implies our result is tight up to a multiplicative constant. On the other hand, a conjecture of Keszegh, Lemons, Martin, Pálvölgyi and Patkós states that given any poset P, either sat* (n, P)= O(1) or sat* (n, P) ≥ n + 1. We prove that this latter conjecture is true for a certain class of posets P. <br/
Humanized H19/Igf2 locus reveals diverged imprinting mechanism between mouse and human and reflects Silver–Russell syndrome phenotypes
Genomic imprinting is essential for mammalian development. Curiously, elements that regulate genomic imprinting, the imprinting control regions (ICRs), often diverge across species. To understand whether the diverged ICR sequence plays a species-specific role at the H19/insulin-like growth factor 2 (Igf2) imprinted locus, we generated a mouse in which the human ICR (hIC1) sequence replaced the endogenous mouse ICR. We show that the imprinting mechanism has partially diverged between mouse and human, depending on the parental origin of the hIC1 in mouse. We also suggest that our mouse model is optimal for studying the imprinting disorders Beckwith–Wiedemann syndrome when hIC1 is maternally transmitted, and Silver–Russell syndrome when hIC1 is paternally transmitted
11.Hypoxic ventilatory depressionと思われる一症例について(第551回千葉医学会例会・第9回麻酔科例会・第18回千葉麻酔懇話会)
FISH analysis on metaphase nuclei (top panel) of cultured cells derived from peripheral blood leukocytes of the proband of family 2 by using BAC probes for 11p15.5-15.4 (RP11-11A9, 3,236,552-3,356,012, green) and 11q22.3 (RP11-179B7, 104,298,339-104,459,797, red). The green signal on both homologues is visible only at chr11p, demonstrating the presence of an in cis duplication and excluding an unbalanced translocation. FISH analysis on interphase nuclei (bottom panel) using the BACs RP11-699D10 (2.9â3.0Â Mb, red) and RP11-11A9 (green), hybridizing within the duplication. Note that single and duplicated signals can be seen on the two homologues, respectively. The red-green-green-red order of the duplicated signals indicates that the duplication is inverted. (PDF 52Â kb
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