Layout of Graphs with Bounded Tree-Width

A \emph{queue layout} of a graph consists of a total order of the vertices, and a partition of the edges into \emph{queues}, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its \emph{queue-number}. A \emph{three-dimensional (straight-line grid) drawing} of a graph represents the vertices by points in $\mathbb{Z}^3$ and the edges by non-crossing line-segments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph $G$ is closely related to the queue-number of $G$. In particular, if $G$ is an $n$-vertex member of a proper minor-closed family of graphs (such as a planar graph), then $G$ has a $O(1)\times O(1)\times O(n)$ drawing if and only if $G$ has O(1) queue-number. (2) It is proved that queue-number is bounded by tree-width, thus resolving an open problem due to Ganley and Heath (2001), and disproving a conjecture of Pemmaraju (1992). This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. (3) It is proved that graphs of bounded tree-width have three-dimensional drawings with O(n) volume. This is the most general family of graphs known to admit three-dimensional drawings with O(n) volume. The proofs depend upon our results regarding \emph{track layouts} and \emph{tree-partitions} of graphs, which may be of independent interest.Comment: This is a revised version of a journal paper submitted in October 2002. This paper incorporates the following conference papers: (1) Dujmovic', Morin & Wood. Path-width and three-dimensional straight-line grid drawings of graphs (GD'02), LNCS 2528:42-53, Springer, 2002. (2) Wood. Queue layouts, tree-width, and three-dimensional graph drawing (FSTTCS'02), LNCS 2556:348--359, Springer, 2002. (3) Dujmovic' & Wood. Tree-partitions of $k$-trees with applications in graph layout (WG '03), LNCS 2880:205-217, 200

Gambaran Adolescent Belief Mengenai Karakteristik Orangtua: suatu Penelitian dengan Pendekatan Indigenous Psychology

Penelitian ini dilakukan sejak tahun 2014, yang bertujuan untuk menemukan gambaran tentang belief remaja terhadap orangtuanya (adolescent belief), sehingga dapat diperoleh pemahaman tentang karakteristik orangtua yang diyakini oleh remaja. Melalui pemahaman ini, diharapkan dapat dijadikan informasi tentang styerotipe remaja akan orangtuanya, yang dapat saja mempengaruhi pola komunikasi antara orangtua dan remaja. Penelitian awal dilakukan dengan memberikan pertanyaan terbuka, terhadap 1029 remaja. Subjek dapat memberikan jawaban lebih dari tiga respon, sehingga diperoleh respon sebanyak 4262 dari remaja. Melalui pengolahan data secara open koding dan kategorisasi, diperoleh 11 kategori besar, yaitu baik, peduli, disiplin, bertanggung jawab, hangat, bijaksana, religius, jujur, tegar, setia dan cerdas.Berdasarkan kategori tersebut, maka dikonstruksikan alat ukur dan dilakukan pengujian validitas terhadap alat ukur tersebut. Berdasarkan pengujian diperoleh nilai validasi untuk keduapuluhtiga aitem adalah 0.31-0.717, dan dengan nilai reliabilitas sebesar 0.89. Hal ini berarti alat ukur tersebut dapat digunakan untuk mengukur adolescent belief terhadap orangtua. Selanjutnya dilakukan penelitian terhadap 208 remaja, dan diperoleh hasil bahwa seluruh remaja memiliki nilai mean>3.0. Hal ini berarti remaja memiliki keyakinan bahwa orangtua memiliki karakteristik-karakteristik yang positif di dalam dirinya

Identifikasi Parenting Belief Pada Remaja Dan Orangtua Di Kota Bandung : Pendekatan Psikologi Psikologi Indigenous

Penelitian ini dilakukan pada tahun 2014, dengan maksud untuk menemukan kebutuhan remaja terhadap gaya pengasuhan orangtua, melalui pemahaman parenting belief remaja,dan dilakukan pula penelitian terhadap parenting belief orangtua untuk menemukan belief orangtua tentang gaya pengasuhan yang tepat bagi remaja. Dengan mengetahui belief remaja dan orangtua, diharapkan dapat memberikan pengetahuan bagi orangtua dan remaja tentang pengasuhan, sehingga dapat meminimalisir konflik yang sering muncul saat orangtua melakukan pengasuhan terhadap remaja. Penelitian dilakukan dengan memberikan pertanyaan terbuka, terhadap 1029 remaja dan 607 orangtua. Subjek dapat memberikan jawaban lebih dari tiga respon, sehingga diperoleh respon sebanyak 3657 dari remaja dan 2285 dari orangtua. Melalui pengolahan data secara open koding dan kategorisasi, diperoleh 5 kategori parenting belief yang dimiliki remaja dan orangtua. Kategori parenting belief remaja dan orangtua adalah directing (mengarahkan), accepting (menerima), nurturing (memelihara), maturing (mendewasakan), modeling (memberi contoh)

A linear-time algorithm for finding a complete graph minor in a dense graph

Let g(t) be the minimum number such that every graph G with average degree d(G) \geq g(t) contains a K_{t}-minor. Such a function is known to exist, as originally shown by Mader. Kostochka and Thomason independently proved that g(t) \in \Theta(t*sqrt{log t}). This article shows that for all fixed \epsilon > 0 and fixed sufficiently large t \geq t(\epsilon), if d(G) \geq (2+\epsilon)g(t) then we can find this K_{t}-minor in linear time. This improves a previous result by Reed and Wood who gave a linear-time algorithm when d(G) \geq 2^{t-2}.Comment: 6 pages, 0 figures; Clarification added in several places, no change to arguments or result

Pertumbuhan Planlet Stroberi (Fragaria Ananassa D) Var. Dorit pada Beberapa Variasi Media Modifikasi In Vitro di Balai Penelitian Jeruk dan Buah Subtropika (BALITJESTRO

  Stroberi (Vragaria ananassa Dutch) Var. Dorit merupakan buah yang populer di masyarakat dunia dengan ciri khas rasa buahnya yang asam manis dan segar. Penyediaan benih stroberi selama ini dilakukan secara konvensional dengan menggunakan stolon, sehingga volume perbanyakan relatif lebih sedikit dan tidak bebas penyakit. Oleh karena  itu  diperlukan metode  kultur jaringan untuk budidaya stroberi. Kultur jaringan tanaman merupakan suatu teknik pengisolasian dan pemeliharaan sel atau potongan jaringan tanaman yang ditumbuhkan pada media buatan yang sesuai dan dalam keadaan aseptik. Medium yang dipergunakan pada kultur in vitro tumbuhan ada bermacam-macam. Medium yang digunakan dalam percobaan ini yaitu media MP yang merupakan kombinasi dari larutan MS (Murashige and skoog) dan pupuk cair. Dalam hal ini pupuk yang digunakan merupakan produk dari Balitjestro yang tentunya mengandung beberapa nutrisi dengan konsentrasi yang tepat untuk petumbuhan tanaman. Percobaan ini dilakukan untuk  mengidentifikasi pengaruh berbagai modifikasi media MP serta mengidentifikasi konsentrasi kombinasi media MP yang sesuai terhadap pertumbuhan stroberi varietas dorit. Percobaan ini  menggunakan Rancangan Acak Kelompok (RAK) dengan perlakuan MP1: MS 25% + pupuk 75%, MP2: MS 50% + pupuk 50%, MP3: MS 75% + pupuk 25%, MP4: pupuk 100%, Percobaan di ulang 5x, sehingga diperlukan 20 unit percobaan. Setiap unit percobaan ditanam 5 planlet. Pertumbuhan tanaman stroberi varietas dorit yang ditanam pada media MP1, MP2, MP3 dan MP4 menunjukkan pengaruh perbedaan yang signifikan terhadap pertumbuhan akar, pertumbuhan tunas dan pertambahan jumlah daun. Tanaman tersebut menunjukkan respon pertumbuhan yang paling cepat pada media MP3 karena mengandung konsentrasi larutan MS lebih banyak sehingga jumlah nitrogen yang dibutuhkan untuk pertumbuhan lebih tercukupi

Analisis terhadap Penolakan Perdamaian pada Penundaan Kewajiban Pembayaran Utang (Pkpu) oleh Kreditur Separatis dalam Perkara Kepailitan

Suspension of Debt Payment is a certain period of time that is given to borrowers who can not pay off debts that have on due time or matured and can be billed, to submit a plan and negotiate to creditors. The peace in negotiation in PKPU ever happened to PT Maja Supreme Latexindo (PT MAL) proposed by one of the unsecured creditors namely Erwito. PT.MAL has a debt owed to unsecured creditors and creditors separatist, but one of the separatist creditors, namely PT. BRI, Putri Hijau Medan branch did not agree with the peace agreed upon by the other creditors by reason that the peace in violation of Article 285 Verse 2 part a, b, and c, 2 of Verse 281 of Law No. 37 of 2004 concerning with Bankruptcy and PKPU ( UUK and PKPU ).The objectives of this paper were, firstly to determine the application process of PKPU request by Erwito and peace proposed by PT . PT MAL against unsecured creditors. Secondly, to determine and analyze the reasons for the PT.BRI to reject peace proposed by PT . MAL. Thirdly, to know peace settlement efforts on PKPU between PT . BRI Putri Hijau Medan Br\qanch and PT . MAL . This type of research was normative juridical research.The conclusions drawn in this study were firstly, the application submitted by Erwito was in conformity with the requirement of the request PKPU namely Article 222 Verse 1 and 3 of UUK and PKPU and peace proposed by PT . MAL was in conformity with Article 281 UUK and PKPU. Secondly, the reason of PT BRI to reject peace agreed upon by debtor and other creditors referring to Article 285 , verse 2 a, b and c were not proven. Thirdly, the legal effort to do by PT BRI was to declare the debtor bankrupt if PT. MAL can not implement the agreement contents as stipulated in Article 255 Verse 1 of the UUK and PKPU and can apply for bankruptcy if it fulfills Article 2 Verse 1 of the UUK and PKPU. PT. BRI can also take legal actions to file an application in a civil case if the debt PT . MAL to PT BRI Putri Hijau Medan branch have not been paid.The suggestions to pose by the author is as follows. Firstly, for business doers, especially before applying for a declaration of bankruptcy should have enough knowledge about PKPU . Secondly , the judges verdict should explain the reason that the proposal is contrary to UUHT and peace achieved because of the conspiracy. Thirdly, bankruptcy regulation should provide an explanation of Article 285 , verse 2 , part b and c . Fourthly ,UUK and PKPU should first set before bankruptcy. Fifthly, the parties involved should do a peace treaty rights

An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains

It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound of ckw^{2} on the number of chains used by First-Fit for some constant c, while Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this paper we prove an upper bound of the form ckw. This is best possible up to the value of c.Comment: v3: referees' comments incorporate