New Invariants for Partitioning a Graph into 2-connected Subgraphs

A vertex partition in which every part induces a 2-connected subgraph is called a 2-proper partition. This concept was introduced by Ferrara et al. in 2013, and Borozan et al. gave the best possible minimum degree condition for the existence of a 2-proper partition in 2016. Later, in 2022, Chen et al. extended the result by showing a minimum degree sum condition for the existence of 2-proper partition. In this paper, we introduce two new invariants of graph, denoted by $\sigma^*(G)$ and $\alpha^*(G)$. These two invariants are defined from degree sum on all independent sets with some property. We prove that if a graph $G$ satisfies $\sigma^*(G)\geq |V(G)|$, then with some exceptions, $G$ has a 2-proper partition with at most $\alpha^*(G)$ parts. This result is best possible, and implies both of the results by Borozan et al. and by Chen et al.. Moreover, as a corollary of our result, we give a minimum degree product condition for the existence of a 2-proper partition.Comment: 14 pages, 4 figure

On a hamiltonian cycle in which specified vertices are not isolated

AbstractLet G be a graph with n vertices and minimum degree at least n/2, and B a set of vertices with at least 3n/4 vertices. In this paper, we show that there exists a hamiltonian cycle in which every vertex in B is adjacent to some vertex in B

セカイ ト ニホン ノ ショクリョウアンゼンホショウ

食料安全保障を,供給の安定性,価格の安価性,品質の安全性の3面からとらえ,その確立に向けての現状の把握と課題の検討を行った。コメ,小麦等主要穀物の需給構造の長期変容パターンの特徴を実証分析するための枠組みとして,自給指向型,輸入依存型,輸出指向型の3つの需給構造変容の5段階モデルを作成し,米国農務省等の統計データを利用して,日本を中心に主要食料の需給構造の変容過程と現段階の特徴をモデルに照らして同定した。それにより,例えば60年代以降の日本のコメ需給は,国内需要が国内生産で賄われる自給指向型の変容過程をとりながらも,その現段階は,需給量が一貫して漸減する「成熟段階」にあることが示唆された。また日本では,食料安全保障の確立には食料自給率の向上が不可欠とする考えが一般的であるのに対し,筆者は,単純な国産比率である「自給率」の意味の「限界」と,上記3側面で見る安全保障への無関係さと無力さを,小麦の自給化政策の効果や生鮮かぼちゃの「自給率の季節変動」の実証分析によって明らかにした。結論として,世界の食料安全保障は,世界各国の自由貿易体制下の協調と国際的な相互協力の結果として保証されるものである以上,日本の食料安全保障もその枠組みの中で,国際協調と自由貿易による便益を活用しつつ,地球規模的な視野でその確立を図るべきことを提言した。The purpose of this study is to discuss the salient feature of the present situation and issues of Japan\u27s and the World\u27s Food Security, in terms of three principal dimensions : 1) stability of demand & supply of food, 2) rationality of food prices and 3) safety of food. As a conceptual framework to undertake the empirical study on the long term changes of food demand & supply structure, 3 types of 5-stage figure models, 1) Self-sufficiency oriented structural change model, 2) Import dependent structural change model and 3) Export oriented structural change model, were established. Using internet statistical data provided by U S Department of Agriculture, FAO of UN and MAFF of Japan, empirical analysis of the structural change of demand & supply relations of major food was conducted comparing the result of analysis with the models established. The result of the analysis identified that the changed pattern of demand & supply of Japanese rice is just at "The mature stage" in the model, in which both the demand volume and the supply decrease in parallel trend in the long run. On the other hand, the author argued that it is inevitably needed to increase self-sufficiency ratios of food to consolidate food security in Japan, because the author does not agree with such opinion, since the concept of "Food Self-sufficiency Ratios" has simple and severe limitations and it is clear that, in any case, there is no relationship between the ratios of food self-sufficiency and the degree of Food Security. In conclusion, it is proposed from the global view point that we should promote international free trade and economic cooperation more in order to develop agriculture and food supply especially in the developing regions of the world. Thus, we in Japan can consolidate our food security

On separable self-complementary graphs

AbstractIn this paper, we describe the structure of separable self-complementary graphs

A pair of forbidden subgraphs and perfect matchings

AbstractIn this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases.(1)Every graph in H is triangle-free.(2)H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases

パルボシクリブ併用内分泌治療が著効した閉経前再発乳癌の１例

　パルボシクリブ併用内分泌療法が著効した閉経前再発乳癌の１例を報告する．８年前に乳房温存手術を受け，残存乳房への放射線治療後に化学内分泌補助療法（シクロフォスファミド＋エピルビシン（CE 90）を４サイクル後に毎週パクリタキセルを４サイクル施行．化学療法終了後からLH-RH アゴニスト２年間とタモキシフェン５年間）を行った．治療継続中も含め定期で外来受診を継続しており，年１回の画像検査（肺，肝，骨を標的）と３か月ごとの腫瘍マーカー測定では再発の兆候はなく経過していた．しかし，補助治療終了後約３年で発熱と肝機能障害をきっかけに多発遠隔再発（肺・骨・肝・子宮体部）を発見した．ホルモン感受性は残存している可能性はあったが，急速な再発であるために，再発後初回治療としてドセタキセルおよびデノスマブの投与を開始した．有効ではあったが投与後約半年でマーカーの再上昇と体動時呼吸困難（在宅酸素療法導入）および疲労・倦怠感の増強が出現した．有害事象と病勢進行のため再発後の二次治療としてパルボシクリブ，フルベストラント，LH-RH アゴニストを導入した．導入後１か月で体動時呼吸困難が消失し，３か月で在宅酸素療法が中止できた．半年後のPET/CT で集積が消失しており画像上は著効と判断できた．有害事象は白血球・好中球減少が出現した以外に認めなかった．再発治療としてパルボシクリブ併用内分泌治療が有用であった．　We have a case of pre-menopausal patient with recurrent breast cancer showing an excellent response to endocrine therapy with palbociclib. Eight years ago, she underwent breast conserving operation followed by adjuvant chemo-endocrine therapy (4 cycles of cyclophosphamide and doxorubicin, 4 cycles of paclitaxel and tamoxifen adding LHRH agonist). The administration of tamoxifen continued for 5 years as an adjuvant therapy. After 3 years of discontinuation of adjuvant medication, fever and liver dysfunction led to find the recurrence of breast cancer in lung, bone, liver and uterus. We chose to treat with chemotherapy as the first line, because the recurrence was rash and multiple. After 6 months of treatment of docetaxel and denosumab, serum decreased tumor markers elevated gradually and dyspnea and general fatigue worsened. She recieved palbociclib, fluvestrant and LH-RH agonist as a second endocrine therapy. Six months after the treatment, PET/CT revealed an excellent effect on each metastatic lesion. Adverse event was only seen in neutropenia to make one-level reduction of dose. Palbociclib and endocrine therapy appeared to be useful as a second-line treatment for recurrent breast patient

ベバシズマブ併用化学療法中に消化管穿孔をきたした再発乳癌の１例

　ベバシズマブはパクリタキセルとの併用でHER2陰性の進行・再発乳癌に対する有効性が示されており，無増悪生存期間を有意に延長させる．しかし，ベバシズマブ特有の有害事象も報告されており，投与の際には注意を要する．今回，再発乳癌に対しベバシズマブを使用し，腸管穿孔を起こした１例を経験した．症例は72歳女性．右乳癌術後５年目に多発リンパ節，肺転移を認め，化学療法で治療中に８次治療としてベバシズマブとパクリタキセル（BP）療法を開始した．１年ほど奏効したが，突然，腹痛を訴え受診した．CT で腹腔内にfree air を認めたため緊急開腹術を施行した．小腸に１か所の穿孔部位を認めた．病理組織検査では，穿孔部に乳癌の転移巣が認められた．乳癌に対するベバシズマブ併用化学療法中の消化管穿孔は報告が少ない．腹膜播種を認める症例やベバシズマブ投与期間の長い患者では，腹部膨満感や腹痛を訴えた際は消化管穿孔を念頭におく必要がある．　Combination therapy with bevacizumab and paclitaxel (BP therapy) has been reported to be effective for the treatment of HER2-negative metastatic breast cancer and to significantly prolong progression-free survival. However, there are specific adverse effects induced by bevacizumab that physicians should pay attention to. We report a recent case of metastatic breast cancer with gastrointestinal perforation during bevacizumab therapy. A 72-year-old female patient had metastases into multiple lymph nodes and lungs five years after surgery for primary breast cancer, and was treated with several chemotherapies. The patient received BP therapy as the eighth treatment regimen. Although the therapy led to stable disease for approximately one year, the patient suddenly developed abdominal pain. Emergency laparotomy was performed because computed tomography revealed free air in the peritoneal cavity. A perforated lesion was found in her small intestine. On pathological examination, breast cancer metastasis was noted around the perforated site. There are few reports of gastrointestinal perforation during bevacizumab therapy for patients with metastatic breast cancer. When a patient has peritoneal dissemination, long-term BP therapy and abdominal pain, physicians should keep in mind the possibility of gastrointestinal perforation during BP therapy. (187 words